LMFDB - Embedded newform 31.4.g.a.7.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,4,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82905921018$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	31.7
Dual form			31.4.g.a.9.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26435 + 3.89127i) q^{2} +(-5.86148 + 1.24590i) q^{3} +(-7.07124 + 5.13756i) q^{4} +(-2.32632 + 4.02930i) q^{5} +(-12.2591 - 21.2333i) q^{6} +(19.5539 + 8.70595i) q^{7} +(-2.45125 - 1.78094i) q^{8} +(8.13897 - 3.62370i) q^{9} +(-18.6204 - 3.95788i) q^{10} +(-1.92247 - 18.2911i) q^{11} +(35.0471 - 38.9237i) q^{12} +(40.8149 + 45.3295i) q^{13} +(-9.15424 + 87.0968i) q^{14} +(8.61558 - 26.5160i) q^{15} +(-17.7769 + 54.7117i) q^{16} +(10.7059 - 101.859i) q^{17} +(24.3913 + 27.0893i) q^{18} +(51.1502 - 56.8080i) q^{19} +(-4.25081 - 40.4438i) q^{20} +(-125.461 - 26.6677i) q^{21} +(68.7449 - 30.6072i) q^{22} +(-124.907 - 90.7499i) q^{23} +(16.5868 + 7.38493i) q^{24} +(51.6765 + 89.5063i) q^{25} +(-124.785 + 216.134i) q^{26} +(87.7037 - 63.7205i) q^{27} +(-182.998 + 38.8973i) q^{28} +(53.9995 + 166.193i) q^{29} +114.074 q^{30} +(-138.386 - 103.152i) q^{31} -259.614 q^{32} +(34.0574 + 104.818i) q^{33} +(409.898 - 87.1266i) q^{34} +(-80.5675 + 58.5357i) q^{35} +(-38.9356 + 67.4385i) q^{36} +(91.0387 + 157.684i) q^{37} +(285.727 + 127.214i) q^{38} +(-295.711 - 214.847i) q^{39} +(12.8783 - 5.73380i) q^{40} +(31.0432 + 6.59844i) q^{41} +(-54.8561 - 521.921i) q^{42} +(207.975 - 230.980i) q^{43} +(107.566 + 119.464i) q^{44} +(-4.33284 + 41.2242i) q^{45} +(195.207 - 600.784i) q^{46} +(21.4556 - 66.0334i) q^{47} +(36.0339 - 342.840i) q^{48} +(77.0491 + 85.5717i) q^{49} +(-282.956 + 314.254i) q^{50} +(64.1541 + 610.386i) q^{51} +(-521.495 - 110.847i) q^{52} +(-58.4726 + 26.0337i) q^{53} +(358.842 + 260.714i) q^{54} +(78.1727 + 34.8047i) q^{55} +(-32.4267 - 56.1647i) q^{56} +(-229.039 + 396.707i) q^{57} +(-578.429 + 420.253i) q^{58} +(685.680 - 145.746i) q^{59} +(75.3048 + 231.764i) q^{60} -136.347 q^{61} +(226.425 - 668.916i) q^{62} +190.696 q^{63} +(-186.027 - 572.531i) q^{64} +(-277.595 + 59.0046i) q^{65} +(-364.814 + 265.053i) q^{66} +(-212.687 + 368.385i) q^{67} +(447.605 + 775.275i) q^{68} +(845.202 + 376.308i) q^{69} +(-329.644 - 239.500i) q^{70} +(-639.647 + 284.789i) q^{71} +(-26.4042 - 5.61239i) q^{72} +(-110.340 - 1049.81i) q^{73} +(-498.485 + 553.623i) q^{74} +(-414.416 - 460.256i) q^{75} +(-69.8407 + 664.490i) q^{76} +(121.650 - 374.399i) q^{77} +(462.144 - 1422.33i) q^{78} +(61.3267 - 583.485i) q^{79} +(-179.095 - 198.906i) q^{80} +(-595.643 + 661.529i) q^{81} +(13.5732 + 129.140i) q^{82} +(-665.419 - 141.439i) q^{83} +(1024.17 - 455.992i) q^{84} +(385.517 + 280.095i) q^{85} +(1161.76 + 517.248i) q^{86} +(-523.577 - 906.862i) q^{87} +(-27.8629 + 48.2599i) q^{88} +(-243.809 + 177.137i) q^{89} +(-165.893 + 35.2616i) q^{90} +(403.453 + 1241.70i) q^{91} +1349.48 q^{92} +(939.662 + 432.211i) q^{93} +284.081 q^{94} +(109.905 + 338.253i) q^{95} +(1521.72 - 323.451i) q^{96} +(828.611 - 602.021i) q^{97} +(-235.565 + 408.011i) q^{98} +(-81.9285 - 141.904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26435	+	3.89127i	0.447015	+	1.37577i	0.880259	+	0.474494i	$0.157369\pi$
$2$	1.26435	+	3.89127i	0.447015	+	1.37577i	−0.433244	+	0.901277i	$0.642631\pi$
$3$	−5.86148	+	1.24590i	−1.12804	+	0.239773i	−0.733887	−	0.679271i	$-0.762296\pi$
$3$	−5.86148	+	1.24590i	−1.12804	+	0.239773i	−0.394155	+	0.919044i	$0.628963\pi$
$4$	−7.07124	+	5.13756i	−0.883905	+	0.642195i
$5$	−2.32632	+	4.02930i	−0.208072	+	0.360392i	−0.951107	−	0.308861i	$-0.900052\pi$
$5$	−2.32632	+	4.02930i	−0.208072	+	0.360392i	0.743035	+	0.669253i	$0.233386\pi$
$6$	−12.2591	−	21.2333i	−0.834124	−	1.44475i
$7$	19.5539	+	8.70595i	1.05581	+	0.470077i	0.859856	−	0.510536i	$-0.170553\pi$
$7$	19.5539	+	8.70595i	1.05581	+	0.470077i	0.195954	+	0.980613i	$0.437220\pi$
$8$	−2.45125	−	1.78094i	−0.108331	−	0.0787071i
$9$	8.13897	−	3.62370i	0.301443	−	0.134211i
$10$	−18.6204	−	3.95788i	−0.588828	−	0.125159i
$11$	−1.92247	−	18.2911i	−0.0526952	−	0.501362i	−0.988758	−	0.149527i	$-0.952225\pi$
$11$	−1.92247	−	18.2911i	−0.0526952	−	0.501362i	0.936062	−	0.351834i	$-0.114442\pi$
$12$	35.0471	−	38.9237i	0.843102	−	0.936359i
$13$	40.8149	+	45.3295i	0.870770	+	0.967088i	0.999698	−	0.0245658i	$-0.00782032\pi$
$13$	40.8149	+	45.3295i	0.870770	+	0.967088i	−0.128928	+	0.991654i	$0.541154\pi$
$14$	−9.15424	+	87.0968i	−0.174755	+	1.66268i
$15$	8.61558	−	26.5160i	0.148302	−	0.456427i
$16$	−17.7769	+	54.7117i	−0.277764	+	0.854871i
$17$	10.7059	−	101.859i	0.152738	−	1.45321i	−0.602689	−	0.797976i	$-0.705904\pi$
$17$	10.7059	−	101.859i	0.152738	−	1.45321i	0.755427	−	0.655232i	$-0.227429\pi$
$18$	24.3913	+	27.0893i	0.319393	+	0.354722i
$19$	51.1502	−	56.8080i	0.617613	−	0.685929i	−0.350465	−	0.936576i	$-0.613977\pi$
$19$	51.1502	−	56.8080i	0.617613	−	0.685929i	0.968079	+	0.250647i	$0.0806433\pi$
$20$	−4.25081	−	40.4438i	−0.0475255	−	0.452175i
$21$	−125.461	−	26.6677i	−1.30371	−	0.277112i
$22$	68.7449	−	30.6072i	0.666203	−	0.296613i
$23$	−124.907	−	90.7499i	−1.13238	−	0.822725i	−0.146343	−	0.989234i	$-0.546750\pi$
$23$	−124.907	−	90.7499i	−1.13238	−	0.822725i	−0.986040	+	0.166509i	$0.946750\pi$
$24$	16.5868	+	7.38493i	0.141074	+	0.0628101i
$25$	51.6765	+	89.5063i	0.413412	+	0.716050i
$26$	−124.785	+	216.134i	−0.941244	+	1.63028i
$27$	87.7037	−	63.7205i	0.625133	−	0.454186i
$28$	−182.998	+	38.8973i	−1.23512	+	0.262532i
$29$	53.9995	+	166.193i	0.345775	+	1.06418i	0.961168	+	0.275964i	$0.0889972\pi$
$29$	53.9995	+	166.193i	0.345775	+	1.06418i	−0.615393	+	0.788220i	$0.711003\pi$
$30$	114.074			0.694233
$31$	−138.386	−	103.152i	−0.801768	−	0.597636i
$31$	−138.386	−	103.152i	−0.801768	−	0.597636i
$32$	−259.614			−1.43418
$33$	34.0574	+	104.818i	0.179655	+	0.552922i
$34$	409.898	−	87.1266i	2.06756	−	0.439473i
$35$	−80.5675	+	58.5357i	−0.389097	+	0.282695i
$36$	−38.9356	+	67.4385i	−0.180257	+	0.312215i
$37$	91.0387	+	157.684i	0.404505	+	0.700623i	0.994264	−	0.106957i	$-0.0341106\pi$
$37$	91.0387	+	157.684i	0.404505	+	0.700623i	−0.589759	+	0.807579i	$0.700777\pi$
$38$	285.727	+	127.214i	1.21976	+	0.543074i
$39$	−295.711	−	214.847i	−1.21415	−	0.882129i
$40$	12.8783	−	5.73380i	0.0509061	−	0.0226649i
$41$	31.0432	+	6.59844i	0.118247	+	0.0251342i	0.266655	−	0.963792i	$-0.414082\pi$
$41$	31.0432	+	6.59844i	0.118247	+	0.0251342i	−0.148408	+	0.988926i	$0.547415\pi$
$42$	−54.8561	−	521.921i	−0.201535	−	1.91748i
$43$	207.975	−	230.980i	0.737580	−	0.819166i	−0.251296	−	0.967910i	$-0.580857\pi$
$43$	207.975	−	230.980i	0.737580	−	0.819166i	0.988876	+	0.148745i	$0.0475233\pi$
$44$	107.566	+	119.464i	0.368549	+	0.409316i
$45$	−4.33284	+	41.2242i	−0.0143534	+	0.136563i
$46$	195.207	−	600.784i	0.625688	−	1.92567i
$47$	21.4556	−	66.0334i	0.0665876	−	0.204935i	−0.912227	−	0.409686i	$-0.865638\pi$
$47$	21.4556	−	66.0334i	0.0665876	−	0.204935i	0.978814	+	0.204750i	$0.0656383\pi$
$48$	36.0339	−	342.840i	0.108355	−	1.03093i
$49$	77.0491	+	85.5717i	0.224633	+	0.249480i
$50$	−282.956	+	314.254i	−0.800320	+	0.888845i
$51$	64.1541	+	610.386i	0.176145	+	1.67590i
$52$	−521.495	−	110.847i	−1.39074	−	0.295610i
$53$	−58.4726	+	26.0337i	−0.151544	+	0.0674717i	−0.481107	−	0.876662i	$-0.659765\pi$
$53$	−58.4726	+	26.0337i	−0.151544	+	0.0674717i	0.329563	+	0.944134i	$0.393099\pi$
$54$	358.842	+	260.714i	0.904299	+	0.657012i
$55$	78.1727	+	34.8047i	0.191651	+	0.0853285i
$56$	−32.4267	−	56.1647i	−0.0773786	−	0.134024i
$57$	−229.039	+	396.707i	−0.532227	+	0.921844i
$58$	−578.429	+	420.253i	−1.30951	+	0.951413i
$59$	685.680	−	145.746i	1.51302	−	0.321601i	0.624711	−	0.780856i	$-0.285217\pi$
$59$	685.680	−	145.746i	1.51302	−	0.321601i	0.888305	+	0.459254i	$0.151883\pi$
$60$	75.3048	+	231.764i	0.162030	+	0.498677i
$61$	−136.347			−0.286189			−0.143094	−	0.989709i	$-0.545705\pi$
$61$	−136.347			−0.286189			−0.143094	+	0.989709i	$0.545705\pi$
$62$	226.425	−	668.916i	0.463807	−	1.37020i
$63$	190.696			0.381357
$64$	−186.027	−	572.531i	−0.363334	−	1.11823i
$65$	−277.595	+	59.0046i	−0.529714	+	0.112594i
$66$	−364.814	+	265.053i	−0.680386	+	0.494329i
$67$	−212.687	+	368.385i	−0.387819	+	0.671721i	−0.992156	−	0.125007i	$-0.960105\pi$
$67$	−212.687	+	368.385i	−0.387819	+	0.671721i	0.604337	+	0.796729i	$0.293438\pi$
$68$	447.605	+	775.275i	0.798237	+	1.38259i
$69$	845.202	+	376.308i	1.47464	+	0.656553i
$70$	−329.644	−	239.500i	−0.562856	−	0.408939i
$71$	−639.647	+	284.789i	−1.06919	+	0.476032i	−0.864415	−	0.502778i	$-0.832311\pi$
$71$	−639.647	+	284.789i	−1.06919	+	0.476032i	−0.204770	+	0.978810i	$0.565645\pi$
$72$	−26.4042	−	5.61239i	−0.0432190	−	0.00918649i
$73$	−110.340	−	1049.81i	−0.176908	−	1.68317i	−0.618371	−	0.785886i	$-0.712207\pi$
$73$	−110.340	−	1049.81i	−0.176908	−	1.68317i	0.441463	−	0.897279i	$-0.354460\pi$
$74$	−498.485	+	553.623i	−0.783076	+	0.869694i
$75$	−414.416	−	460.256i	−0.638035	−	0.708610i
$76$	−69.8407	+	664.490i	−0.105412	+	1.00292i
$77$	121.650	−	374.399i	0.180042	−	0.554114i
$78$	462.144	−	1422.33i	0.670866	−	2.06471i
$79$	61.3267	−	583.485i	0.0873392	−	0.830977i	−0.859903	−	0.510458i	$-0.829476\pi$
$79$	61.3267	−	583.485i	0.0873392	−	0.830977i	0.947242	−	0.320519i	$-0.103857\pi$
$80$	−179.095	−	198.906i	−0.250293	−	0.277979i
$81$	−595.643	+	661.529i	−0.817069	+	0.907447i
$82$	13.5732	+	129.140i	0.0182793	+	0.173916i
$83$	−665.419	−	141.439i	−0.879990	−	0.187048i	−0.254306	−	0.967124i	$-0.581847\pi$
$83$	−665.419	−	141.439i	−0.879990	−	0.187048i	−0.625685	+	0.780076i	$0.715180\pi$
$84$	1024.17	−	455.992i	1.33032	−	0.592295i
$85$	385.517	+	280.095i	0.491944	+	0.357418i
$86$	1161.76	+	517.248i	1.45669	+	0.648562i
$87$	−523.577	−	906.862i	−0.645211	−	1.11754i
$88$	−27.8629	+	48.2599i	−0.0337522	+	0.0584605i
$89$	−243.809	+	177.137i	−0.290378	+	0.210972i	−0.723431	−	0.690396i	$-0.757436\pi$
$89$	−243.809	+	177.137i	−0.290378	+	0.210972i	0.433053	+	0.901368i	$0.357436\pi$
$90$	−165.893	+	35.2616i	−0.194296	+	0.0412989i
$91$	403.453	+	1241.70i	0.464762	+	1.43039i
$92$	1349.48			1.52927
$93$	939.662	+	432.211i	1.04772	+	0.481916i
$94$	284.081			0.311710
$95$	109.905	+	338.253i	0.118695	+	0.365306i
$96$	1521.72	−	323.451i	1.61781	−	0.343876i
$97$	828.611	−	602.021i	0.867348	−	0.630165i	−0.0625261	−	0.998043i	$-0.519916\pi$
$97$	828.611	−	602.021i	0.867348	−	0.630165i	0.929874	+	0.367878i	$0.119916\pi$
$98$	−235.565	+	408.011i	−0.242813	+	0.420565i
$99$	−81.9285	−	141.904i	−0.0831729	−	0.144060i
$100$	−825.261	−	367.430i	−0.825261	−	0.367430i
$101$	−1142.80	−	830.291i	−1.12587	−	0.817991i	−0.140779	−	0.990041i	$-0.544961\pi$
$101$	−1142.80	−	830.291i	−1.12587	−	0.817991i	−0.985088	+	0.172050i	$0.944961\pi$
$102$	−2294.06	+	1021.38i	−2.22692	+	0.991488i
$103$	73.7854	+	15.6836i	0.0705854	+	0.0150034i	0.243069	−	0.970009i	$-0.421846\pi$
$103$	73.7854	+	15.6836i	0.0705854	+	0.0150034i	−0.172484	+	0.985012i	$0.555179\pi$
$104$	−19.3185	−	183.803i	−0.0182147	−	0.173301i
$105$	399.315	−	443.485i	0.371135	−	0.412187i
$106$	−175.234	−	194.617i	−0.160568	−	0.178329i
$107$	158.392	−	1507.00i	0.143106	−	1.36156i	−0.653436	−	0.756981i	$-0.726673\pi$
$107$	158.392	−	1507.00i	0.143106	−	1.36156i	0.796543	−	0.604582i	$-0.206660\pi$
$108$	−292.807	+	901.166i	−0.260883	+	0.802914i
$109$	−650.562	+	2002.22i	−0.571675	+	1.75943i	0.0755570	+	0.997141i	$0.475927\pi$
$109$	−650.562	+	2002.22i	−0.571675	+	1.75943i	−0.647232	+	0.762293i	$0.724073\pi$
$110$	−36.5969	+	348.196i	−0.0317216	+	0.301811i
$111$	−730.079	−	810.835i	−0.624289	−	0.693343i
$112$	−823.926	+	915.062i	−0.695122	+	0.772011i
$113$	−76.0520	−	723.586i	−0.0633130	−	0.602383i	−0.979474	−	0.201572i	$-0.935395\pi$
$113$	−76.0520	−	723.586i	−0.0633130	−	0.602383i	0.916161	−	0.400811i	$-0.131272\pi$
$114$	−1833.28	−	389.675i	−1.50616	−	0.320144i
$115$	656.231	−	292.173i	0.532121	−	0.236915i
$116$	−1235.67	−	897.768i	−0.989046	−	0.718584i
$117$	496.452	+	221.034i	0.392282	+	0.174655i
$118$	1434.07	+	2483.89i	1.11879	+	1.93780i
$119$	1096.12	−	1898.54i	0.844383	−	1.46251i
$120$	−68.3424	+	49.6536i	−0.0519898	+	0.0377728i
$121$	971.046	−	206.402i	0.729561	−	0.155073i
$122$	−172.391	−	530.564i	−0.127931	−	0.393730i
$123$	−190.180			−0.139414
$124$	1508.51	+	18.4506i	1.09249	+	0.0133622i
$125$	−1062.44			−0.760223
$126$	241.107	+	742.050i	0.170472	+	0.524659i
$127$	−108.294	+	23.0187i	−0.0756660	+	0.0160833i	−0.245589	−	0.969374i	$-0.578981\pi$
$127$	−108.294	+	23.0187i	−0.0756660	+	0.0160833i	0.169923	+	0.985457i	$0.445648\pi$
$128$	312.416	−	226.983i	0.215734	−	0.156740i
$129$	−931.266	+	1613.00i	−0.635608	+	1.10091i
$130$	−580.579	−	1005.59i	−0.391694	−	0.678433i
$131$	795.174	+	354.034i	0.530341	+	0.236123i	0.654395	−	0.756152i	$-0.272923\pi$
$131$	795.174	+	354.034i	0.530341	+	0.236123i	−0.124055	+	0.992275i	$0.539590\pi$
$132$	−779.335	−	566.220i	−0.513882	−	0.373357i
$133$	1494.75	−	665.506i	0.974522	−	0.433885i
$134$	−1702.39	−	361.855i	−1.09750	−	0.233280i
$135$	52.7223	+	501.619i	0.0336120	+	0.319796i
$136$	−207.648	+	230.617i	−0.130924	+	0.145406i
$137$	1530.71	+	1700.03i	0.954581	+	1.06017i	0.998131	+	0.0611186i	$0.0194668\pi$
$137$	1530.71	+	1700.03i	0.954581	+	1.06017i	−0.0435493	+	0.999051i	$0.513867\pi$
$138$	−395.685	+	3764.69i	−0.244079	+	2.32226i
$139$	−707.274	+	2176.77i	−0.431584	+	1.32828i	0.464962	+	0.885331i	$0.346068\pi$
$139$	−707.274	+	2176.77i	−0.431584	+	1.32828i	−0.896546	+	0.442950i	$0.853932\pi$
$140$	268.982	−	827.840i	0.162379	−	0.499752i
$141$	−43.4906	+	413.785i	−0.0259756	+	0.247142i
$142$	−1916.93	−	2128.96i	−1.13285	−	1.25816i
$143$	750.662	−	833.694i	0.438975	−	0.487532i
$144$	53.5732	+	509.715i	0.0310030	+	0.294974i
$145$	−795.264	−	169.039i	−0.455470	−	0.0968130i
$146$	3945.59	−	1756.69i	2.23657	−	0.995785i
$147$	−558.235	−	405.582i	−0.313214	−	0.227563i
$148$	−1453.87	−	647.303i	−0.807480	−	0.359513i
$149$	1.04114	+	1.80330i	0.000572439	+	0.000991493i	0.866311	−	0.499504i	$-0.166484\pi$
$149$	1.04114	+	1.80330i	0.000572439	+	0.000991493i	−0.865739	+	0.500496i	$0.833151\pi$
$150$	1267.01	−	2194.53i	0.689674	−	1.19455i
$151$	−528.432	+	383.928i	−0.284789	+	0.206911i	−0.721004	−	0.692931i	$-0.756319\pi$
$151$	−528.432	+	383.928i	−0.284789	+	0.206911i	0.436214	+	0.899843i	$0.356319\pi$
$152$	−226.553	+	48.1554i	−0.120894	+	0.0256968i
$153$	−281.974	−	867.825i	−0.148995	−	0.458559i
$154$	1610.70			0.842815
$155$	737.561	−	317.633i	0.382209	−	0.164599i
$156$	3194.84			1.63969
$157$	144.596	+	445.021i	0.0735033	+	0.226220i	0.981058	−	0.193714i	$-0.0620533\pi$
$157$	144.596	+	445.021i	0.0735033	+	0.226220i	−0.907555	+	0.419934i	$0.862053\pi$
$158$	2348.03	−	499.090i	1.18228	−	0.251300i
$159$	310.301	−	225.447i	0.154770	−	0.112447i
$160$	603.944	−	1046.06i	0.298412	−	0.516865i
$161$	−1652.34	−	2861.94i	−0.808838	−	1.40095i
$162$	−3327.29	−	1481.40i	−1.61368	−	0.718457i
$163$	544.238	+	395.412i	0.261521	+	0.190006i	0.710818	−	0.703376i	$-0.248325\pi$
$163$	544.238	+	395.412i	0.261521	+	0.190006i	−0.449296	+	0.893383i	$0.648325\pi$
$164$	−253.414	+	112.827i	−0.120660	+	0.0537214i
$165$	−501.571	−	106.612i	−0.236650	−	0.0503015i
$166$	−290.944	−	2768.15i	−0.136034	−	1.29428i
$167$	−1531.27	+	1700.64i	−0.709539	+	0.788023i	−0.984864	−	0.173328i	$-0.944548\pi$
$167$	−1531.27	+	1700.64i	−0.709539	+	0.788023i	0.275325	+	0.961351i	$0.411215\pi$
$168$	260.044	+	288.808i	0.119422	+	0.132631i
$169$	−159.262	+	1515.27i	−0.0724905	+	0.689701i
$170$	−602.495	+	1854.29i	−0.271819	+	0.836573i
$171$	210.454	−	647.711i	0.0941160	−	0.289659i
$172$	−283.971	+	2701.80i	−0.125887	+	1.19773i
$173$	839.689	+	932.569i	0.369020	+	0.409838i	0.898843	−	0.438270i	$-0.144409\pi$
$173$	839.689	+	932.569i	0.369020	+	0.409838i	−0.529824	+	0.848108i	$0.677742\pi$
$174$	2866.86	−	3183.97i	1.24906	−	1.38722i
$175$	231.239	+	2200.09i	0.0998857	+	0.950349i
$176$	1034.91	+	219.978i	0.443236	+	0.0942128i
$177$	−3837.52	+	1708.57i	−1.62963	+	0.725560i
$178$	−997.548	−	724.761i	−0.420053	−	0.305186i
$179$	−1163.60	−	518.066i	−0.485873	−	0.216324i	0.149155	−	0.988814i	$-0.452345\pi$
$179$	−1163.60	−	518.066i	−0.485873	−	0.216324i	−0.635028	+	0.772489i	$0.719011\pi$
$180$	−181.153	−	313.767i	−0.0750132	−	0.129927i
$181$	703.946	−	1219.27i	0.289082	−	0.500705i	−0.684509	−	0.729005i	$-0.739983\pi$
$181$	703.946	−	1219.27i	0.289082	−	0.500705i	0.973591	+	0.228300i	$0.0733166\pi$
$182$	−4321.68	+	3139.89i	−1.76013	+	1.27881i
$183$	799.198	−	169.875i	0.322833	−	0.0686202i
$184$	144.557	+	444.902i	0.0579180	+	0.178253i
$185$	−847.141			−0.336665
$186$	−493.788	+	4202.94i	−0.194657	+	1.65685i
$187$	−1883.70			−0.736632
$188$	187.533	+	577.167i	0.0727514	+	0.223906i
$189$	2269.70	−	482.439i	0.873525	−	0.185673i
$190$	−1177.27	+	855.340i	−0.449518	+	0.326594i
$191$	6.95235	−	12.0418i	0.00263379	−	0.00456187i	−0.864706	−	0.502279i	$-0.832495\pi$
$191$	6.95235	−	12.0418i	0.00263379	−	0.00456187i	0.867339	+	0.497717i	$0.165828\pi$
$192$	1803.71	+	3124.11i	0.677976	+	1.17429i
$193$	−2095.48	−	932.966i	−0.781532	−	0.347961i	−0.0231175	−	0.999733i	$-0.507359\pi$
$193$	−2095.48	−	932.966i	−0.781532	−	0.347961i	−0.758415	+	0.651772i	$0.774026\pi$
$194$	3390.28	+	2463.18i	1.25468	+	0.911578i
$195$	1553.60	−	691.709i	0.570543	−	0.254022i
$196$	−984.462	−	209.254i	−0.358769	−	0.0762587i
$197$	121.795	+	1158.81i	0.0440485	+	0.419094i	0.994220	+	0.107365i	$0.0342413\pi$
$197$	121.795	+	1158.81i	0.0440485	+	0.419094i	−0.950171	+	0.311729i	$0.899092\pi$
$198$	448.601	−	498.222i	0.161014	−	0.178824i
$199$	1001.64	+	1112.44i	0.356807	+	0.396275i	0.894648	−	0.446772i	$-0.147426\pi$
$199$	1001.64	+	1112.44i	0.356807	+	0.396275i	−0.537841	+	0.843047i	$0.680760\pi$
$200$	32.7331	−	311.435i	0.0115729	−	0.110109i
$201$	787.691	−	2424.26i	0.276415	−	0.850719i
$202$	1785.99	−	5496.71i	0.622088	−	1.91459i
$203$	−390.972	+	3719.85i	−0.135176	+	1.28612i
$204$	−3589.54	−	3986.59i	−1.23195	−	1.36822i
$205$	−98.8035	+	109.732i	−0.0336621	+	0.0373856i
$206$	32.2616	+	306.948i	0.0109115	+	0.103816i
$207$	−1345.46	−	285.986i	−0.451768	−	0.0960263i
$208$	−3205.62	+	1427.23i	−1.06860	+	0.475773i
$209$	−1137.42	−	826.381i	−0.376444	−	0.273502i
$210$	2230.59	+	993.123i	0.732978	+	0.326343i
$211$	−2677.31	−	4637.23i	−0.873523	−	1.51299i	−0.858328	−	0.513102i	$-0.828496\pi$
$211$	−2677.31	−	4637.23i	−0.873523	−	1.51299i	−0.0151951	−	0.999885i	$-0.504837\pi$
$212$	279.724	−	484.496i	0.0906205	−	0.156959i
$213$	3394.46	−	2466.22i	1.09195	−	0.793346i
$214$	6064.41	−	1289.03i	1.93717	−	0.411758i
$215$	446.871	+	1375.33i	0.141751	+	0.436264i
$216$	−328.466			−0.103469
$217$	−1807.94	−	3221.81i	−0.565580	−	1.00788i
$218$	−8613.73			−2.67613
$219$	1954.71	+	6015.98i	0.603137	+	1.85626i
$220$	−731.590	+	155.504i	−0.224199	+	0.0476549i
$221$	5054.20	−	3672.09i	1.53838	−	1.11770i
$222$	2232.10	−	3866.11i	0.674814	−	1.16881i
$223$	508.328	+	880.449i	0.152646	+	0.264391i	0.932200	−	0.361945i	$-0.117887\pi$
$223$	508.328	+	880.449i	0.152646	+	0.264391i	−0.779553	+	0.626336i	$0.784554\pi$
$224$	−5076.45	−	2260.18i	−1.51422	−	0.674173i
$225$	744.937	+	541.228i	0.220722	+	0.160364i
$226$	2719.51	−	1210.80i	0.800438	−	0.356378i
$227$	4908.59	+	1043.35i	1.43522	+	0.305065i	0.858893	−	0.512155i	$-0.171153\pi$
$227$	4908.59	+	1043.35i	1.43522	+	0.305065i	0.576325	+	0.817220i	$0.304486\pi$
$228$	−418.515	−	3981.91i	−0.121565	−	1.15662i
$229$	−1616.89	+	1795.74i	−0.466582	+	0.518192i	−0.929806	−	0.368049i	$-0.880026\pi$
$229$	−1616.89	+	1795.74i	−0.466582	+	0.518192i	0.463224	+	0.886241i	$0.346692\pi$
$230$	1966.63	+	2184.16i	0.563807	+	0.626171i
$231$	−246.585	+	2346.10i	−0.0702341	+	0.668233i
$232$	163.614	−	503.552i	0.0463008	−	0.142499i
$233$	902.919	−	2778.90i	0.253872	−	0.781338i	−0.740178	−	0.672411i	$-0.765259\pi$
$233$	902.919	−	2778.90i	0.253872	−	0.781338i	0.994050	−	0.108926i	$-0.0347413\pi$
$234$	−232.416	+	2211.29i	−0.0649295	+	0.617763i
$235$	216.156	+	240.066i	0.0600020	+	0.0666390i
$236$	−4099.83	+	4553.32i	−1.13083	+	1.25592i
$237$	367.496	+	3496.49i	0.100723	+	0.958319i
$238$	8773.62	+	1864.89i	2.38954	+	0.507912i
$239$	−3136.84	+	1396.61i	−0.848976	+	0.377989i	−0.784649	−	0.619940i	$-0.787157\pi$
$239$	−3136.84	+	1396.61i	−0.848976	+	0.377989i	−0.0643274	+	0.997929i	$0.520490\pi$
$240$	1297.58	+	942.747i	0.348993	+	0.253559i
$241$	−6826.74	−	3039.46i	−1.82469	−	0.812402i	−0.933208	−	0.359338i	$-0.883003\pi$
$241$	−6826.74	−	3039.46i	−1.82469	−	0.812402i	−0.891478	−	0.453065i	$-0.850331\pi$
$242$	2030.91	+	3517.63i	0.539469	+	0.934388i
$243$	1203.65	−	2084.78i	0.317754	−	0.550365i
$244$	964.146	−	700.493i	0.252964	−	0.183789i
$245$	−524.035	+	111.387i	−0.136651	+	0.0290460i
$246$	−240.454	−	740.041i	−0.0623203	−	0.191802i
$247$	4662.77			1.20115
$248$	155.510	+	499.309i	0.0398182	+	0.127847i
$249$	4076.56			1.03752
$250$	−1343.30	−	4134.25i	−0.339831	−	1.04589i
$251$	−2848.38	+	605.442i	−0.716288	+	0.152252i	−0.551618	−	0.834097i	$-0.685989\pi$
$251$	−2848.38	+	605.442i	−0.716288	+	0.152252i	−0.164670	+	0.986349i	$0.552656\pi$
$252$	−1348.46	+	979.713i	−0.337083	+	0.244905i
$253$	−1419.79	+	2459.14i	−0.352811	+	0.611087i
$254$	−226.494	−	392.299i	−0.0559508	−	0.0969096i
$255$	−2608.67	−	1161.46i	−0.640633	−	0.285228i
$256$	−2617.94	−	1902.04i	−0.639145	−	0.464366i
$257$	3700.29	−	1647.47i	0.898122	−	0.399870i	0.0948568	−	0.995491i	$-0.469761\pi$
$257$	3700.29	−	1647.47i	0.898122	−	0.399870i	0.803266	+	0.595621i	$0.203094\pi$
$258$	−7454.06	−	1584.41i	−1.79872	−	0.382330i
$259$	407.374	+	3875.91i	0.0977336	+	0.929873i
$260$	1659.80	−	1843.40i	0.395909	−	0.439702i
$261$	1041.74	+	1156.96i	0.247057	+	0.274384i
$262$	−372.264	+	3541.86i	−0.0877807	+	0.835178i
$263$	384.960	−	1184.79i	0.0902573	−	0.277783i	−0.895731	−	0.444596i	$-0.853347\pi$
$263$	384.960	−	1184.79i	0.0902573	−	0.277783i	0.985989	+	0.166812i	$0.0533474\pi$
$264$	103.191	−	317.589i	0.0240567	−	0.0740388i
$265$	31.1283	−	296.166i	0.00721584	−	0.0686542i
$266$	4479.55	+	4975.05i	1.03255	+	1.14677i
$267$	1208.39	−	1342.05i	0.276974	−	0.307610i
$268$	−388.636	−	3697.63i	−0.0885811	−	0.842793i
$269$	−3321.12	−	705.927i	−0.752760	−	0.160004i	−0.184477	−	0.982837i	$-0.559059\pi$
$269$	−3321.12	−	705.927i	−0.752760	−	0.160004i	−0.568284	+	0.822833i	$0.692392\pi$
$270$	−1885.27	+	839.378i	−0.424941	+	0.189196i
$271$	5610.35	+	4076.16i	1.25758	+	0.913686i	0.998636	−	0.0522056i	$-0.0166251\pi$
$271$	5610.35	+	4076.16i	1.25758	+	0.913686i	0.258945	+	0.965892i	$0.416625\pi$
$272$	5382.59	+	2396.48i	1.19988	+	0.534221i
$273$	−3911.86	−	6775.54i	−0.867240	−	1.50210i
$274$	−4679.91	+	8105.84i	−1.03184	+	1.78720i
$275$	1537.82	−	1117.29i	0.337215	−	0.245001i
$276$	−7909.93	+	1681.31i	−1.72508	+	0.366677i
$277$	−2640.78	−	8127.49i	−0.572813	−	1.76294i	−0.643509	−	0.765439i	$-0.722522\pi$
$277$	−2640.78	−	8127.49i	−0.572813	−	1.76294i	0.0706961	−	0.997498i	$-0.477478\pi$
$278$	−9364.62			−2.02033
$279$	−1500.11	−	338.085i	−0.321897	−	0.0725470i
$280$	301.740			0.0644014
$281$	200.901	+	618.309i	0.0426503	+	0.131264i	0.970114	−	0.242648i	$-0.0780161\pi$
$281$	200.901	+	618.309i	0.0426503	+	0.131264i	−0.927464	+	0.373912i	$0.878016\pi$
$282$	−1665.13	+	353.935i	−0.351622	+	0.0747395i
$283$	2224.26	−	1616.02i	0.467203	−	0.339443i	−0.329147	−	0.944279i	$-0.606761\pi$
$283$	2224.26	−	1616.02i	0.467203	−	0.339443i	0.796350	+	0.604836i	$0.206761\pi$
$284$	3059.98	−	5300.04i	0.639353	−	1.10739i
$285$	−1065.63	−	1845.73i	−0.221483	−	0.383620i
$286$	4193.23	+	1866.94i	0.866960	+	0.385996i
$287$	549.570	+	399.286i	0.113032	+	0.0821223i
$288$	−2112.99	+	940.762i	−0.432322	+	0.192482i
$289$	−5455.09	−	1159.52i	−1.11034	−	0.236010i
$290$	−347.717	−	3308.31i	−0.0704092	−	0.669898i
$291$	−4106.83	+	4561.10i	−0.827309	+	0.918819i
$292$	6173.70	+	6856.59i	1.23729	+	1.37415i
$293$	−545.723	+	5192.21i	−0.108811	+	1.03526i	0.794789	+	0.606886i	$0.207581\pi$
$293$	−545.723	+	5192.21i	−0.108811	+	1.03526i	−0.903600	+	0.428378i	$0.859085\pi$
$294$	872.422	−	2685.04i	0.173064	−	0.532635i
$295$	−1007.86	+	3101.86i	−0.198914	+	0.612195i
$296$	57.6662	−	548.657i	0.0113236	−	0.107737i
$297$	−1334.13	−	1481.70i	−0.260653	−	0.289484i
$298$	−5.70078	+	6.33135i	−0.00110818	+	0.00123076i
$299$	−984.396	−	9365.90i	−0.190398	−	1.81152i
$300$	5295.03	+	1125.49i	1.01903	+	0.216601i
$301$	6077.63	−	2705.93i	1.16382	−	0.518164i
$302$	−2162.09	−	1570.85i	−0.411968	−	0.299312i
$303$	7732.94	+	3442.93i	1.46616	+	0.652776i
$304$	2198.77	+	3808.39i	0.414830	+	0.718506i
$305$	317.188	−	549.385i	0.0595479	−	0.103140i
$306$	3020.43	−	2194.47i	0.564269	−	0.409965i
$307$	−518.583	+	110.228i	−0.0964075	+	0.0204921i	−0.255863	−	0.966713i	$-0.582360\pi$
$307$	−518.583	+	110.228i	−0.0964075	+	0.0204921i	0.159455	+	0.987205i	$0.449026\pi$
$308$	1063.28	+	3272.45i	0.196708	+	0.605406i
$309$	−452.032			−0.0832207
$310$	2168.53	+	2468.45i	0.397304	+	0.452253i
$311$	−9640.99			−1.75785			−0.878923	−	0.476963i	$-0.841738\pi$
$311$	−9640.99			−1.75785			−0.878923	+	0.476963i	$0.841738\pi$
$312$	342.234	+	1053.29i	0.0621000	+	0.191124i
$313$	1444.36	−	307.009i	0.260832	−	0.0554414i	−0.0756397	−	0.997135i	$-0.524100\pi$
$313$	1444.36	−	307.009i	0.260832	−	0.0554414i	0.336471	+	0.941694i	$0.390767\pi$
$314$	−1548.87	+	1125.32i	−0.278370	+	0.202247i
$315$	−443.620	+	768.373i	−0.0793497	+	0.137438i
$316$	2564.03	+	4441.03i	0.456449	+	0.790594i
$317$	8537.81	+	3801.28i	1.51272	+	0.673505i	0.984465	−	0.175582i	$-0.0561808\pi$
$317$	8537.81	+	3801.28i	1.51272	+	0.673505i	0.528252	+	0.849087i	$0.322848\pi$
$318$	1269.60	+	922.419i	0.223886	+	0.162663i
$319$	2936.05	−	1307.21i	0.515321	−	0.229436i
$320$	2739.66	+	582.333i	0.478599	+	0.101729i
$321$	949.154	+	9030.60i	0.165036	+	1.57021i
$322$	9047.45	−	10048.2i	1.56582	−	1.73902i
$323$	−5238.83	−	5818.31i	−0.902465	−	1.00229i
$324$	813.294	−	7737.98i	0.139454	−	1.32681i
$325$	−1948.11	+	5995.66i	−0.332497	+	1.02332i
$326$	−850.546	+	2617.71i	−0.144501	+	0.444729i
$327$	1318.69	−	12546.5i	0.223009	−	2.12179i
$328$	−64.3433	−	71.4605i	−0.0108316	−	0.0120297i
$329$	994.423	−	1104.42i	0.166639	−	0.185072i
$330$	−219.304	−	2086.54i	−0.0365827	−	0.348062i
$331$	−5795.31	−	1231.83i	−0.962353	−	0.204554i	−0.300161	−	0.953889i	$-0.597040\pi$
$331$	−5795.31	−	1231.83i	−0.962353	−	0.204554i	−0.662192	+	0.749334i	$0.730374\pi$
$332$	5431.99	−	2418.48i	0.897949	−	0.399793i
$333$	1312.36	+	953.485i	0.215967	+	0.156909i
$334$	−8553.72	−	3808.36i	−1.40131	−	0.623905i
$335$	−989.555	−	1713.96i	−0.161389	−	0.279533i
$336$	3689.35	−	6390.14i	0.599020	−	1.03753i
$337$	−1260.28	+	915.646i	−0.203714	+	0.148007i	−0.684965	−	0.728576i	$-0.740183\pi$
$337$	−1260.28	+	915.646i	−0.203714	+	0.148007i	0.481251	+	0.876583i	$0.340183\pi$
$338$	−6097.69	+	1296.10i	−0.981275	+	0.208576i
$339$	1347.29	+	4146.53i	0.215855	+	0.664332i
$340$	−4165.09			−0.664364
$341$	−1620.73	+	2729.54i	−0.257382	+	0.433468i
$342$	2786.50			0.440576
$343$	−1507.09	−	4638.33i	−0.237245	−	0.730165i
$344$	−921.161	+	195.799i	−0.144377	+	0.0306883i
$345$	−3482.47	+	2530.16i	−0.543449	+	0.394839i
$346$	−2567.22	+	4446.55i	−0.398885	+	0.690890i
$347$	−1711.17	−	2963.84i	−0.264728	−	0.458522i	0.702764	−	0.711423i	$-0.251949\pi$
$347$	−1711.17	−	2963.84i	−0.264728	−	0.458522i	−0.967492	+	0.252900i	$0.918615\pi$
$348$	8361.39	+	3722.73i	1.28798	+	0.573447i
$349$	−211.077	−	153.357i	−0.0323745	−	0.0235215i	0.571480	−	0.820616i	$-0.306369\pi$
$349$	−211.077	−	153.357i	−0.0323745	−	0.0235215i	−0.603855	+	0.797094i	$0.706369\pi$
$350$	−8268.77	+	3681.49i	−1.26281	+	0.562240i
$351$	6468.04	+	1374.82i	0.983585	+	0.209067i
$352$	499.100	+	4748.62i	0.0755742	+	0.719041i
$353$	−165.923	+	184.277i	−0.0250176	+	0.0277848i	−0.755524	−	0.655121i	$-0.772618\pi$
$353$	−165.923	+	184.277i	−0.0250176	+	0.0277848i	0.730506	+	0.682906i	$0.239284\pi$
$354$	−11500.5	−	12772.6i	−1.72668	−	1.91767i
$355$	340.521	−	3239.84i	0.0509098	−	0.484375i
$356$	813.977	−	2505.16i	0.121182	−	0.372959i
$357$	−4059.52	+	12493.9i	−0.601829	+	1.85224i
$358$	544.742	−	5182.88i	0.0804205	−	0.765150i
$359$	3807.16	+	4228.28i	0.559706	+	0.621616i	0.954881	−	0.296990i	$-0.0959827\pi$
$359$	3807.16	+	4228.28i	0.559706	+	0.621616i	−0.395175	+	0.918606i	$0.629316\pi$
$360$	84.0387	−	93.3345i	0.0123034	−	0.0136643i
$361$	106.150	+	1009.95i	0.0154760	+	0.147244i
$362$	5634.54	+	1197.66i	0.818079	+	0.173888i
$363$	−5434.61	+	2419.64i	−0.785793	+	0.349858i
$364$	−9232.22	−	6707.60i	−1.32940	−	0.965862i
$365$	4486.69	+	1997.60i	0.643409	+	0.286464i
$366$	1671.49	+	2895.11i	0.238717	+	0.413470i
$367$	−2741.96	+	4749.21i	−0.389998	+	0.675496i	−0.992449	−	0.122660i	$-0.960857\pi$
$367$	−2741.96	+	4749.21i	−0.389998	+	0.675496i	0.602451	+	0.798156i	$0.294191\pi$
$368$	7185.54	−	5220.60i	1.01786	−	0.739518i
$369$	276.570	−	58.7868i	0.0390181	−	0.00829355i
$370$	−1071.08	−	3296.45i	−0.150494	−	0.463174i
$371$	−1370.01			−0.191719
$372$	−8865.09	+	1771.30i	−1.23557	+	0.246875i
$373$	13074.6			1.81495			0.907473	−	0.420110i	$-0.138008\pi$
$373$	13074.6			1.81495			0.907473	+	0.420110i	$0.138008\pi$
$374$	−2381.66	−	7330.00i	−0.329285	−	1.01344i
$375$	6227.49	−	1323.69i	0.857564	−	0.182281i
$376$	−170.194	+	123.653i	−0.0233434	+	0.0169600i
$377$	−5329.49	+	9230.94i	−0.728070	+	1.26105i
$378$	4746.99	+	8222.02i	0.645923	+	1.11877i
$379$	7499.44	+	3338.96i	1.01641	+	0.452536i	0.846196	−	0.532871i	$-0.178887\pi$
$379$	7499.44	+	3338.96i	1.01641	+	0.452536i	0.170216	+	0.985407i	$0.445554\pi$
$380$	−2514.96	−	1827.23i	−0.339512	−	0.246670i
$381$	606.087	−	269.847i	0.0814981	−	0.0362853i
$382$	55.6482	+	11.8284i	0.00745342	+	0.00158427i
$383$	268.701	+	2556.52i	0.0358485	+	0.341076i	0.997715	+	0.0675578i	$0.0215207\pi$
$383$	268.701	+	2556.52i	0.0358485	+	0.341076i	−0.961867	+	0.273518i	$0.911813\pi$
$384$	−1548.42	+	1719.70i	−0.205775	+	0.228536i
$385$	1225.57	+	1361.14i	0.162236	+	0.180182i
$386$	981.007	−	9333.66i	0.129357	−	1.23075i
$387$	855.702	−	2633.58i	0.112397	−	0.345923i
$388$	−2766.39	+	8514.08i	−0.361965	+	1.11401i
$389$	−475.074	+	4520.03i	−0.0619208	+	0.589137i	0.918936	+	0.394407i	$0.129050\pi$
$389$	−475.074	+	4520.03i	−0.0619208	+	0.589137i	−0.980857	+	0.194731i	$0.937617\pi$
$390$	4655.92	+	5170.92i	0.604517	+	0.671384i
$391$	−10581.0	+	11751.4i	−1.36855	+	1.51993i
$392$	−36.4688	−	346.978i	−0.00469886	−	0.0447067i
$393$	−5101.98	−	1084.46i	−0.654863	−	0.139195i
$394$	−4355.23	+	1939.07i	−0.556886	+	0.247942i
$395$	2208.37	+	1604.48i	0.281304	+	0.204380i
$396$	1308.38	+	582.527i	0.166031	+	0.0739219i
$397$	1782.86	+	3088.01i	0.225389	+	0.390385i	0.956436	−	0.291942i	$-0.0943014\pi$
$397$	1782.86	+	3088.01i	0.225389	+	0.390385i	−0.731047	+	0.682327i	$0.760968\pi$
$398$	−3062.37	+	5304.18i	−0.385685	+	0.668026i
$399$	−7932.31	+	5763.16i	−0.995268	+	0.723105i
$400$	−5815.69	+	1236.16i	−0.726962	+	0.154520i
$401$	−242.715	−	746.998i	−0.0302259	−	0.0930257i	0.934805	−	0.355160i	$-0.115574\pi$
$401$	−242.715	−	746.998i	−0.0302259	−	0.0930257i	−0.965031	+	0.262134i	$0.915574\pi$
$402$	10429.4			1.29396
$403$	−972.350	−	10483.1i	−0.120189	−	1.29578i
$404$	12346.7			1.52047
$405$	−1279.84	−	3938.95i	−0.157027	−	0.483279i
$406$	−14969.2	+	3181.81i	−1.82983	+	0.388942i
$407$	2709.19	−	1968.34i	0.329950	−	0.239723i
$408$	929.801	−	1610.46i	0.112824	−	0.195416i
$409$	−4248.31	−	7358.29i	−0.513607	−	0.889594i	−0.999875	−	0.0157844i	$-0.994975\pi$
$409$	−4248.31	−	7358.29i	−0.513607	−	0.889594i	0.486268	−	0.873810i	$-0.338358\pi$
$410$	−551.920	−	245.731i	−0.0664815	−	0.0295994i
$411$	−11090.3	−	8057.58i	−1.33101	−	0.967034i
$412$	−602.330	+	268.174i	−0.0720259	+	0.0320680i
$413$	14676.6	+	3119.60i	1.74864	+	0.371684i
$414$	−588.282	−	5597.13i	−0.0698370	−	0.664454i
$415$	2117.88	−	2352.14i	0.250512	−	0.278222i
$416$	−10596.1	−	11768.2i	−1.24884	−	1.38697i
$417$	1433.65	−	13640.3i	0.168360	−	1.60184i
$418$	1777.58	−	5470.82i	0.208001	−	0.640160i
$419$	2136.14	−	6574.36i	0.249063	−	0.766536i	−0.745879	−	0.666081i	$-0.767970\pi$
$419$	2136.14	−	6574.36i	0.249063	−	0.766536i	0.994942	−	0.100454i	$-0.0320296\pi$
$420$	−545.227	+	5187.49i	−0.0633438	+	0.602676i
$421$	−4332.26	−	4811.46i	−0.501523	−	0.556998i	0.438225	−	0.898865i	$-0.355607\pi$
$421$	−4332.26	−	4811.46i	−0.501523	−	0.556998i	−0.939748	+	0.341867i	$0.888941\pi$
$422$	14659.6	−	16281.2i	1.69104	−	1.87809i
$423$	−64.6593	−	615.192i	−0.00743225	−	0.0707132i
$424$	189.695	+	40.3210i	0.0217274	+	0.00461830i
$425$	9670.30	−	4305.50i	1.10371	−	0.491405i
$426$	13888.5	+	10090.6i	1.57958	+	1.14763i
$427$	−2666.12	−	1187.03i	−0.302161	−	0.134531i
$428$	6622.28	+	11470.1i	0.747897	+	1.29540i
$429$	−3361.29	+	5821.93i	−0.378286	+	0.655211i
$430$	−4786.77	+	3477.79i	−0.536834	+	0.390033i
$431$	10772.6	−	2289.79i	1.20394	−	0.255906i	0.438095	−	0.898929i	$-0.355653\pi$
$431$	10772.6	−	2289.79i	1.20394	−	0.255906i	0.765847	+	0.643023i	$0.222320\pi$
$432$	1927.16	+	5931.18i	0.214631	+	0.660565i
$433$	2213.38			0.245654			0.122827	−	0.992428i	$-0.460804\pi$
$433$	2213.38			0.245654			0.122827	+	0.992428i	$0.460804\pi$
$434$	10251.0	−	11108.7i	1.13379	−	1.22865i
$435$	4872.03			0.537002
$436$	−5686.26	−	17500.5i	−0.624593	−	1.92230i
$437$	−11544.3	+	2453.82i	−1.26371	+	0.268609i
$438$	−20938.3	+	15212.6i	−2.28418	+	1.65956i
$439$	5050.14	−	8747.09i	0.549043	−	0.950970i	−0.449298	−	0.893382i	$-0.648326\pi$
$439$	5050.14	−	8747.09i	0.549043	−	0.950970i	0.998340	−	0.0575880i	$-0.0183410\pi$
$440$	−129.636	−	224.536i	−0.0140458	−	0.0243280i
$441$	937.186	+	417.262i	0.101197	+	0.0450559i
$442$	20679.4	+	15024.4i	2.22538	+	1.61683i
$443$	−3571.33	+	1590.06i	−0.383022	+	0.170532i	−0.589210	−	0.807980i	$-0.700561\pi$
$443$	−3571.33	+	1590.06i	−0.383022	+	0.170532i	0.206188	+	0.978512i	$0.433894\pi$
$444$	9328.28	+	1982.79i	0.997073	+	0.211934i
$445$	−146.563	−	1394.46i	−0.0156130	−	0.148547i
$446$	−2783.36	+	3091.23i	−0.295507	+	0.328193i
$447$	−8.34934	−	9.27288i	−0.000883468	−	0.000981191i
$448$	1346.89	−	12814.8i	0.142041	−	1.35143i
$449$	−232.692	+	716.153i	−0.0244575	+	0.0752725i	−0.962540	−	0.271139i	$-0.912600\pi$
$449$	−232.692	+	716.153i	−0.0244575	+	0.0752725i	0.938083	+	0.346411i	$0.112600\pi$
$450$	−1164.20	+	3583.05i	−0.121958	+	0.375348i
$451$	61.0130	−	580.500i	0.00637027	−	0.0606090i
$452$	4255.25	+	4725.93i	0.442810	+	0.491790i
$453$	2619.06	−	2908.76i	0.271642	−	0.301690i
$454$	2146.21	+	20419.8i	0.221864	+	2.11090i
$455$	−5941.75	−	1262.96i	−0.612205	−	0.130128i
$456$	1267.94	−	564.524i	0.130212	−	0.0579743i
$457$	−960.294	−	697.694i	−0.0982947	−	0.0714152i	0.537552	−	0.843230i	$-0.319349\pi$
$457$	−960.294	−	697.694i	−0.0982947	−	0.0714152i	−0.635847	+	0.771815i	$0.719349\pi$
$458$	−9032.03	−	4021.32i	−0.921482	−	0.410270i
$459$	−5551.59	−	9615.64i	−0.564545	−	0.977820i
$460$	−3139.31	+	5437.45i	−0.318198	+	0.551136i
$461$	583.679	−	424.067i	0.0589688	−	0.0428433i	−0.557910	−	0.829901i	$-0.688397\pi$
$461$	583.679	−	424.067i	0.0589688	−	0.0428433i	0.616879	+	0.787058i	$0.288397\pi$
$462$	−9441.06	+	2006.76i	−0.950731	+	0.202084i
$463$	−4.23023	−	13.0193i	−0.000424613	−	0.00130682i	0.950844	−	0.309670i	$-0.100219\pi$
$463$	−4.23023	−	13.0193i	−0.000424613	−	0.00130682i	−0.951269	+	0.308364i	$0.900219\pi$
$464$	−10052.7			−1.00578
$465$	−3927.46	+	2780.72i	−0.391681	+	0.277318i
$466$	11955.0			1.18843
$467$	3786.41	+	11653.4i	0.375191	+	1.15472i	0.943350	+	0.331800i	$0.107656\pi$
$467$	3786.41	+	11653.4i	0.375191	+	1.15472i	−0.568159	+	0.822919i	$0.692344\pi$
$468$	−4646.11	+	987.560i	−0.458902	+	0.0975427i
$469$	−7365.99	+	5351.71i	−0.725224	+	0.526906i
$470$	−660.863	+	1144.65i	−0.0648582	+	0.112338i
$471$	−1402.00	−	2428.33i	−0.137156	−	0.237561i
$472$	−1940.34	−	863.894i	−0.189219	−	0.0842457i
$473$	−4624.71	−	3360.05i	−0.449565	−	0.326628i
$474$	−13141.1	+	5850.81i	−1.27340	+	0.566955i
$475$	7727.93	+	1642.62i	0.746488	+	0.158671i
$476$	2002.91	+	19056.5i	0.192864	+	1.83498i
$477$	−381.568	+	423.774i	−0.0366264	+	0.0406778i
$478$	−9400.65	−	10440.5i	−0.899531	−	0.999030i
$479$	1561.80	−	14859.5i	0.148978	−	1.41743i	−0.623220	−	0.782047i	$-0.714176\pi$
$479$	1561.80	−	14859.5i	0.148978	−	1.41743i	0.772197	−	0.635383i	$-0.219158\pi$
$480$	−2236.72	+	6883.92i	−0.212691	+	0.654597i
$481$	−3431.99	+	10562.6i	−0.325333	+	1.00127i
$482$	3195.97	−	30407.6i	0.302017	−	2.87350i
$483$	13250.9	+	14716.6i	1.24831	+	1.38639i
$484$	−5806.09	+	6448.32i	−0.545276	+	0.605590i
$485$	498.112	+	4739.22i	0.0466353	+	0.443705i
$486$	9634.27	+	2047.83i	0.899217	+	0.191134i
$487$	−1192.74	+	531.043i	−0.110982	+	0.0494124i	−0.461477	−	0.887152i	$-0.652680\pi$
$487$	−1192.74	+	531.043i	−0.110982	+	0.0494124i	0.350495	+	0.936565i	$0.386014\pi$
$488$	334.222	+	242.826i	0.0310031	+	0.0225251i
$489$	−3682.68	−	1639.64i	−0.340566	−	0.151630i
$490$	−1096.00	−	1898.33i	−0.101045	−	0.175016i
$491$	−8027.92	+	13904.8i	−0.737872	+	1.27803i	0.215580	+	0.976486i	$0.430836\pi$
$491$	−8027.92	+	13904.8i	−0.737872	+	1.27803i	−0.953452	+	0.301545i	$0.902498\pi$
$492$	1344.81	−	977.061i	0.123229	−	0.0895311i
$493$	17506.5	−	3721.12i	1.59930	−	0.339941i
$494$	5895.37	+	18144.1i	0.536933	+	1.65251i
$495$	762.367			0.0692239
$496$	8103.71	−	5737.59i	0.733604	−	0.519406i
$497$	−14987.0			−1.35263
$498$	5154.19	+	15863.0i	0.463785	+	1.42738i
$499$	−8293.86	+	1762.92i	−0.744057	+	0.158154i	−0.564315	−	0.825560i	$-0.690860\pi$
$499$	−8293.86	+	1762.92i	−0.744057	+	0.158154i	−0.179742	+	0.983714i	$0.557526\pi$
$500$	7512.80	−	5458.37i	0.671965	−	0.488211i
$501$	6856.67	−	11876.1i	0.611444	−	1.05905i
$502$	−5957.29	−	10318.3i	−0.529655	−	0.917389i
$503$	−18607.2	−	8284.48i	−1.64942	−	0.734367i	−0.649748	−	0.760150i	$-0.725126\pi$
$503$	−18607.2	−	8284.48i	−1.64942	−	0.734367i	−0.999668	+	0.0257828i	$0.991792\pi$
$504$	−467.444	−	339.618i	−0.0413127	−	0.0300155i
$505$	6004.01	−	2673.16i	0.529059	−	0.235552i
$506$	−11364.3	−	2415.55i	−0.998428	−	0.212222i
$507$	−954.364	−	9080.17i	−0.0835992	−	0.795393i
$508$	647.517	−	719.140i	0.0565530	−	0.0628084i
$509$	2752.01	+	3056.42i	0.239648	+	0.266156i	0.850956	−	0.525236i	$-0.176023\pi$
$509$	2752.01	+	3056.42i	0.239648	+	0.266156i	−0.611308	+	0.791393i	$0.709356\pi$
$510$	1221.26	−	11619.5i	0.106036	−	1.00886i
$511$	6982.04	−	21488.5i	0.604437	−	1.86026i
$512$	5046.03	−	15530.1i	0.435557	−	1.34051i
$513$	866.226	−	8241.59i	0.0745513	−	0.709308i
$514$	11089.2	+	12315.8i	0.951603	+	1.05686i
$515$	−234.842	+	260.819i	−0.0200940	+	0.0223166i
$516$	−1701.67	−	16190.4i	−0.145178	−	1.38128i
$517$	−1249.07	−	265.499i	−0.106256	−	0.0225853i
$518$	−14567.1	+	6485.70i	−1.23560	+	0.550126i
$519$	−6083.71	−	4420.07i	−0.514538	−	0.373833i
$520$	785.538	+	349.744i	0.0662464	+	0.0294948i
$521$	7757.29	+	13436.0i	0.652310	+	1.12983i	0.982561	+	0.185940i	$0.0595331\pi$
$521$	7757.29	+	13436.0i	0.652310	+	1.12983i	−0.330252	+	0.943893i	$0.607134\pi$
$522$	−3184.94	+	5516.48i	−0.267052	+	0.462547i
$523$	80.2491	−	58.3044i	0.00670946	−	0.00487471i	−0.584425	−	0.811447i	$-0.698680\pi$
$523$	80.2491	−	58.3044i	0.00670946	−	0.00487471i	0.591135	+	0.806573i	$0.298680\pi$
$524$	−7441.73	+	1581.79i	−0.620408	+	0.131872i
$525$	−4096.48	−	12607.7i	−0.340543	−	1.04808i
$526$	5097.04			0.422513
$527$	−11988.6	+	12991.6i	−0.990950	+	1.07385i
$528$	−6340.20			−0.522579
$529$	3606.29	+	11099.0i	0.296399	+	0.912223i
$530$	1191.82	−	253.329i	0.0976780	−	0.0207621i
$531$	5052.59	−	3670.92i	0.412926	−	0.300008i
$532$	−7150.67	+	12385.3i	−0.582746	+	1.00935i
$533$	967.921	+	1676.49i	0.0786591	+	0.136242i
$534$	6750.09	+	3005.33i	0.547013	+	0.243546i
$535$	5703.69	+	4143.98i	0.460920	+	0.334878i
$536$	1177.42	−	524.221i	0.0948820	−	0.0422442i
$537$	7465.85	+	1586.92i	0.599954	+	0.127524i
$538$	−1452.11	−	13815.9i	−0.116366	−	1.10715i
$539$	1417.08	−	1573.82i	0.113243	−	0.125769i
$540$	−2949.91	−	3276.21i	−0.235081	−	0.261084i
$541$	−1065.90	+	10141.4i	−0.0847073	+	0.805936i	0.866872	+	0.498532i	$0.166127\pi$
$541$	−1065.90	+	10141.4i	−0.0847073	+	0.805936i	−0.951579	+	0.307405i	$0.900539\pi$
$542$	−8767.98	+	26985.1i	−0.694865	+	2.13857i
$543$	−2607.08	+	8023.77i	−0.206042	+	0.634131i
$544$	−2779.39	+	26444.1i	−0.219054	+	2.08416i
$545$	−6554.16	−	7279.13i	−0.515136	−	0.572117i
$546$	21419.5	−	23788.7i	1.67888	−	1.86459i
$547$	1783.11	+	16965.1i	0.139379	+	1.32610i	0.810931	+	0.585142i	$0.198961\pi$
$547$	1783.11	+	16965.1i	0.139379	+	1.32610i	−0.671552	+	0.740958i	$0.734372\pi$
$548$	−19558.0	−	4157.19i	−1.52459	−	0.324063i
$549$	−1109.73	+	494.082i	−0.0862696	+	0.0384097i
$550$	6292.03	+	4571.43i	0.487806	+	0.354412i
$551$	12203.2	+	5433.22i	0.943510	+	0.420078i
$552$	−1401.62	−	2427.68i	−0.108074	−	0.187190i
$553$	6278.97	−	10875.5i	0.482837	−	0.836298i
$554$	28287.4	−	20552.0i	2.16934	−	1.57612i
$555$	4965.50	−	1055.45i	0.379772	−	0.0807231i
$556$	−6181.96	−	19026.1i	−0.471535	−	1.45124i
$557$	15030.8			1.14340			0.571702	−	0.820462i	$-0.306284\pi$
$557$	15030.8			1.14340			0.571702	+	0.820462i	$0.306284\pi$
$558$	−581.084	−	6264.78i	−0.0440846	−	0.475286i
$559$	18958.7			1.43447
$560$	−1770.35	−	5448.57i	−0.133591	−	0.411150i
$561$	11041.3	−	2346.90i	0.830952	−	0.176624i
$562$	−2152.00	+	1563.52i	−0.161524	+	0.117354i
$563$	2951.15	−	5111.54i	0.220917	−	0.382639i	−0.734170	−	0.678966i	$-0.762428\pi$
$563$	2951.15	−	5111.54i	0.220917	−	0.382639i	0.955087	+	0.296327i	$0.0957618\pi$
$564$	−1818.31	−	3149.41i	−0.135753	−	0.235131i
$565$	3092.47	+	1376.86i	0.230267	+	0.102522i
$566$	9100.60	+	6611.97i	0.675842	+	0.491028i
$567$	−17406.4	+	7749.82i	−1.28924	+	0.574007i
$568$	2075.13	+	441.082i	0.153293	+	0.0325834i
$569$	2570.95	+	24460.9i	0.189420	+	1.80221i	0.515525	+	0.856874i	$0.327597\pi$
$569$	2570.95	+	24460.9i	0.189420	+	1.80221i	−0.326106	+	0.945333i	$0.605737\pi$
$570$	5834.91	−	6480.32i	0.428767	−	0.476194i
$571$	3057.35	+	3395.53i	0.224074	+	0.248859i	0.844691	−	0.535255i	$-0.179784\pi$
$571$	3057.35	+	3395.53i	0.224074	+	0.248859i	−0.620617	+	0.784114i	$0.713118\pi$
$572$	−1024.96	+	9751.82i	−0.0749224	+	0.712839i
$573$	−25.7482	+	79.2449i	−0.00187722	+	0.00577749i
$574$	−858.879	+	2643.36i	−0.0624546	+	0.192215i
$575$	1667.96	−	15869.6i	0.120972	−	1.15097i
$576$	−3588.75	−	3985.71i	−0.259603	−	0.288318i
$577$	−5620.57	+	6242.28i	−0.405524	+	0.450380i	−0.910967	−	0.412480i	$-0.864663\pi$
$577$	−5620.57	+	6242.28i	−0.405524	+	0.450380i	0.505442	+	0.862860i	$0.331329\pi$
$578$	−2385.16	−	22693.3i	−0.171643	−	1.63307i
$579$	13445.0	+	2857.82i	0.965033	+	0.205124i
$580$	6491.95	−	2890.40i	0.464765	−	0.206927i
$581$	−11780.2	−	8558.79i	−0.841176	−	0.611150i
$582$	−22940.9	−	10214.0i	−1.63390	−	0.727461i
$583$	588.597	+	1019.48i	0.0418133	+	0.0724228i
$584$	−1599.18	+	2769.86i	−0.113313	+	0.196263i
$585$	−2045.52	+	1486.16i	−0.144567	+	0.105034i
$586$	−20894.3	+	4441.21i	−1.47292	+	0.313080i
$587$	1883.43	+	5796.60i	0.132432	+	0.407583i	0.995182	−	0.0980477i	$-0.0312598\pi$
$587$	1883.43	+	5796.60i	0.132432	+	0.407583i	−0.862750	+	0.505631i	$0.831260\pi$
$588$	6031.12			0.422992
$589$	−12938.3	+	2585.16i	−0.905118	+	0.180848i
$590$	−13344.5			−0.931157
$591$	−2157.65	−	6640.57i	−0.150176	−	0.462194i
$592$	−10245.5	+	2177.76i	−0.711299	+	0.151191i
$593$	−9202.05	+	6685.68i	−0.637240	+	0.462982i	−0.858901	−	0.512142i	$-0.828852\pi$
$593$	−9202.05	+	6685.68i	−0.637240	+	0.462982i	0.221661	+	0.975124i	$0.428852\pi$
$594$	4078.88	−	7064.83i	0.281748	−	0.488002i
$595$	5099.87	+	8833.24i	0.351385	+	0.608617i
$596$	−16.6267	−	7.40269i	−0.00114271	−	0.000508769i
$597$	−7257.10	−	5272.59i	−0.497510	−	0.361462i
$598$	35200.6	−	15672.3i	2.40712	−	1.07172i
$599$	−16162.7	−	3435.49i	−1.10249	−	0.234341i	−0.379494	−	0.925194i	$-0.623902\pi$
$599$	−16162.7	−	3435.49i	−1.10249	−	0.234341i	−0.722995	+	0.690853i	$0.757235\pi$
$600$	196.151	+	1866.25i	0.0133464	+	0.126982i
$601$	9437.57	−	10481.5i	0.640543	−	0.711395i	−0.332218	−	0.943202i	$-0.607797\pi$
$601$	9437.57	−	10481.5i	0.640543	−	0.711395i	0.972762	+	0.231807i	$0.0744638\pi$
$602$	18213.8	+	20228.4i	1.23312	+	1.36952i
$603$	−396.136	+	3768.98i	−0.0267528	+	0.254535i
$604$	1764.22	−	5429.70i	0.118849	−	0.365780i
$605$	−1427.31	+	4392.79i	−0.0959144	+	0.295194i
$606$	−3620.21	+	34444.0i	−0.242675	+	2.30890i
$607$	−13885.5	−	15421.4i	−0.928492	−	1.03119i	−0.999432	−	0.0337141i	$-0.989266\pi$
$607$	−13885.5	−	15421.4i	−0.928492	−	1.03119i	0.0709396	−	0.997481i	$-0.477400\pi$
$608$	−13279.3	+	14748.1i	−0.885766	+	0.983743i
$609$	−2342.87	−	22290.9i	−0.155891	−	1.48321i
$610$	2538.84	+	539.647i	0.168516	+	0.0358191i
$611$	3868.97	−	1722.58i	0.256173	−	0.114056i
$612$	6452.41	+	4687.95i	0.426181	+	0.309639i
$613$	−13812.2	−	6149.60i	−0.910066	−	0.405188i	−0.102343	−	0.994749i	$-0.532634\pi$
$613$	−13812.2	−	6149.60i	−0.910066	−	0.405188i	−0.807723	+	0.589562i	$0.799301\pi$
$614$	−1084.60	−	1878.58i	−0.0712880	−	0.123474i
$615$	442.420	−	766.293i	0.0290083	−	0.0502438i
$616$	−964.976	+	701.096i	−0.0631169	+	0.0458571i
$617$	−14330.9	+	3046.12i	−0.935072	+	0.198756i	−0.650159	−	0.759798i	$-0.725298\pi$
$617$	−14330.9	+	3046.12i	−0.935072	+	0.198756i	−0.284913	+	0.958553i	$0.591965\pi$
$618$	−571.526	−	1758.98i	−0.0372009	−	0.114493i
$619$	−15395.3			−0.999657			−0.499829	−	0.866124i	$-0.666604\pi$
$619$	−15395.3			−0.999657			−0.499829	+	0.866124i	$0.666604\pi$
$620$	−3583.62	+	6035.32i	−0.232132	+	0.390942i
$621$	−16737.4			−1.08156
$622$	−12189.6	−	37515.7i	−0.785784	−	2.41839i
$623$	−6309.56	+	1341.14i	−0.405758	+	0.0862465i
$624$	17011.5	−	12359.6i	1.09135	−	0.792915i
$625$	−3987.98	+	6907.38i	−0.255230	+	0.442072i
$626$	3020.83	+	5232.24i	0.192870	+	0.334061i
$627$	7696.53	+	3426.72i	0.490223	+	0.218261i
$628$	−3308.79	−	2403.98i	−0.210247	−	0.152753i
$629$	17036.2	−	7585.01i	1.07993	−	0.480818i
$630$	−3550.83	−	754.753i	−0.224553	−	0.0477303i
$631$	1592.41	+	15150.8i	0.100464	+	0.955852i	0.922391	+	0.386259i	$0.126233\pi$
$631$	1592.41	+	15150.8i	0.100464	+	0.955852i	−0.821926	+	0.569594i	$0.807101\pi$
$632$	−1189.48	+	1321.05i	−0.0748653	+	0.0831464i
$633$	21470.5	+	23845.4i	1.34814	+	1.49727i
$634$	−3997.01	+	38029.0i	−0.250381	+	2.38222i
$635$	159.178	−	489.900i	0.00994771	−	0.0306159i
$636$	−1035.97	+	3188.37i	−0.0645892	+	0.198785i
$637$	−734.174	+	6985.20i	−0.0456657	+	0.434480i
$638$	8798.91	+	9772.18i	0.546007	+	0.606402i
$639$	−4174.08	+	4635.78i	−0.258410	+	0.286993i
$640$	187.806	+	1786.85i	0.0115995	+	0.110362i
$641$	19384.7	+	4120.34i	1.19446	+	0.253890i	0.761888	−	0.647709i	$-0.224273\pi$
$641$	19384.7	+	4120.34i	1.19446	+	0.253890i	0.432573	+	0.901599i	$0.357606\pi$
$642$	−33940.4	+	15111.2i	−2.08648	+	0.928961i
$643$	−13262.4	−	9635.68i	−0.813401	−	0.590970i	0.101414	−	0.994844i	$-0.467663\pi$
$643$	−13262.4	−	9635.68i	−0.813401	−	0.590970i	−0.914815	+	0.403874i	$0.867663\pi$
$644$	26387.5	+	11748.5i	1.61462	+	0.718874i
$645$	−4332.85	−	7504.71i	−0.264505	−	0.458136i
$646$	16016.9	−	27742.0i	0.975504	−	1.68962i
$647$	−8268.00	+	6007.05i	−0.502393	+	0.365010i	−0.809930	−	0.586526i	$-0.800495\pi$
$647$	−8268.00	+	6007.05i	−0.502393	+	0.365010i	0.307537	+	0.951536i	$0.400495\pi$
$648$	2638.21	−	560.769i	0.159936	−	0.0339955i
$649$	−3984.05	−	12261.7i	−0.240967	−	0.741621i
$650$	−25793.8			−1.55649
$651$	14611.2	+	16632.1i	0.879661	+	1.00132i
$652$	−5879.89			−0.353181
$653$	5881.63	+	18101.8i	0.352475	+	1.08481i	0.957459	+	0.288569i	$0.0931793\pi$
$653$	5881.63	+	18101.8i	0.352475	+	1.08481i	−0.604984	+	0.796237i	$0.706821\pi$
$654$	50489.2	−	10731.8i	3.01878	−	0.641662i
$655$	−3276.34	+	2380.40i	−0.195446	+	0.142000i
$656$	−912.865	+	1581.13i	−0.0543314	+	0.0941047i
$657$	−4702.25	−	8144.54i	−0.279227	−	0.483636i
$658$	5554.89	+	2473.20i	0.329106	+	0.146528i
$659$	6999.86	+	5085.70i	0.413772	+	0.300623i	0.775127	−	0.631805i	$-0.217686\pi$
$659$	6999.86	+	5085.70i	0.413772	+	0.300623i	−0.361355	+	0.932428i	$0.617686\pi$
$660$	4094.46	−	1822.97i	0.241479	−	0.107514i
$661$	−27281.5	−	5798.86i	−1.60534	−	0.341225i	−0.683846	−	0.729626i	$-0.739694\pi$
$661$	−27281.5	−	5798.86i	−1.60534	−	0.341225i	−0.921490	+	0.388401i	$0.873028\pi$
$662$	−2533.91	−	24108.5i	−0.148766	−	1.41542i
$663$	−25050.0	+	27820.9i	−1.46736	+	1.62967i
$664$	1379.21	+	1531.77i	0.0806083	+	0.0895246i
$665$	−795.743	+	7570.99i	−0.0464024	+	0.441489i
$666$	−2050.98	+	6312.28i	−0.119330	+	0.367261i
$667$	8337.15	−	25659.1i	0.483982	−	1.48954i
$668$	2090.80	−	19892.6i	0.121101	−	1.15220i
$669$	−4076.50	−	4527.41i	−0.235585	−	0.261644i
$670$	5418.33	−	6017.67i	0.312431	−	0.346989i
$671$	262.124	+	2493.95i	0.0150808	+	0.143484i
$672$	32571.5	+	6923.28i	1.86975	+	0.397428i
$673$	26879.5	−	11967.5i	1.53957	−	0.685460i	0.550761	−	0.834663i	$-0.314337\pi$
$673$	26879.5	−	11967.5i	1.53957	−	0.685460i	0.988807	+	0.149203i	$0.0476708\pi$
$674$	−5156.46	−	3746.39i	−0.294687	−	0.214103i
$675$	10235.6	+	4557.19i	0.583657	+	0.259861i
$676$	−6658.63	−	11533.1i	−0.378848	−	0.656183i
$677$	4696.11	−	8133.91i	0.266597	−	0.461760i	−0.701384	−	0.712784i	$-0.747434\pi$
$677$	4696.11	−	8133.91i	0.266597	−	0.461760i	0.967981	+	0.251024i	$0.0807673\pi$
$678$	−14431.8	+	10485.3i	−0.817479	+	0.593933i
$679$	21443.7	−	4558.01i	1.21198	−	0.257615i
$680$	−446.168	−	1373.17i	−0.0251614	−	0.0774390i
$681$	−30071.5			−1.69213
$682$	−12670.5	−	2855.60i	−0.711406	−	0.160332i
$683$	15487.5			0.867664			0.433832	−	0.900994i	$-0.357161\pi$
$683$	15487.5			0.867664			0.433832	+	0.900994i	$0.357161\pi$
$684$	1839.48	+	5661.34i	0.102828	+	0.316472i
$685$	−10410.9	+	2212.90i	−0.580698	+	0.123431i
$686$	16143.5	−	11728.9i	0.898487	−	0.652789i
$687$	7240.08	−	12540.2i	0.402076	−	0.696416i
$688$	8940.16	+	15484.8i	0.495407	+	0.858071i
$689$	−3566.64	−	1587.97i	−0.197211	−	0.0878040i
$690$	−14248.6	−	10352.2i	−0.786137	−	0.571162i
$691$	3081.35	−	1371.90i	0.169638	−	0.0755278i	−0.320161	−	0.947363i	$-0.603737\pi$
$691$	3081.35	−	1371.90i	0.169638	−	0.0755278i	0.489799	+	0.871835i	$0.337070\pi$
$692$	−10728.8	−	2280.47i	−0.589374	−	0.125275i
$693$	−366.608	−	3488.05i	−0.0200957	−	0.191198i
$694$	9369.57	−	10406.0i	0.512484	−	0.569171i
$695$	−7125.51	−	7913.68i	−0.388901	−	0.431918i
$696$	−331.646	+	3155.41i	−0.0180618	+	0.171847i
$697$	1004.46	−	3091.40i	0.0545861	−	0.167999i
$698$	329.876	−	1015.25i	0.0178883	−	0.0550544i
$699$	−1830.22	+	17413.4i	−0.0990348	+	0.942254i
$700$	−12938.2	−	14369.4i	−0.698599	−	0.775872i
$701$	12989.3	−	14426.1i	0.699857	−	0.777270i	−0.283496	−	0.958973i	$-0.591494\pi$
$701$	12989.3	−	14426.1i	0.699857	−	0.777270i	0.983353	+	0.181703i	$0.0581610\pi$
$702$	2828.05	+	26907.1i	0.152048	+	1.44664i
$703$	13614.3	+	2893.82i	0.730405	+	0.155252i
$704$	−10114.6	+	4503.31i	−0.541489	+	0.241087i
$705$	−1566.09	−	1137.83i	−0.0836630	−	0.0607848i
$706$	−926.854	−	412.662i	−0.0494088	−	0.0219982i
$707$	−15117.7	−	26184.6i	−0.804184	−	1.39289i
$708$	18358.1	−	31797.2i	0.974492	−	1.68787i
$709$	2548.11	−	1851.31i	0.134973	−	0.0980640i	−0.518250	−	0.855229i	$-0.673416\pi$
$709$	2548.11	−	1851.31i	0.134973	−	0.0980640i	0.653223	+	0.757165i	$0.273416\pi$
$710$	13037.6	−	2771.23i	0.689146	−	0.146482i
$711$	−1615.24	−	4971.19i	−0.0851986	−	0.262214i
$712$	913.107			0.0480620
$713$	7924.21	+	25442.9i	0.416219	+	1.33639i
$714$	−53749.9			−2.81728
$715$	1612.93	+	4964.08i	0.0843638	+	0.259645i
$716$	10889.7	−	2314.67i	0.568388	−	0.120815i
$717$	16646.5	−	12094.4i	0.867050	−	0.629949i
$718$	−11639.8	+	20160.7i	−0.605004	+	1.04790i
$719$	−1702.76	−	2949.27i	−0.0883203	−	0.152975i	0.818481	−	0.574534i	$-0.194817\pi$
$719$	−1702.76	−	2949.27i	−0.0883203	−	0.152975i	−0.906801	+	0.421558i	$0.861483\pi$
$720$	−2178.43	−	969.898i	−0.112757	−	0.0502027i
$721$	1306.25	+	949.047i	0.0674720	+	0.0490213i
$722$	−3795.77	+	1689.99i	−0.195657	+	0.0871119i
$723$	43801.7	+	9310.33i	2.25311	+	0.478914i
$724$	1286.30	+	12238.3i	0.0660289	+	0.628223i
$725$	−12084.9	+	13421.6i	−0.619062	+	0.687538i
$726$	−16286.7	−	18088.2i	−0.832585	−	0.924680i
$727$	−1292.60	+	12298.3i	−0.0659420	+	0.627396i	0.910781	+	0.412891i	$0.135481\pi$
$727$	−1292.60	+	12298.3i	−0.0659420	+	0.627396i	−0.976723	+	0.214506i	$0.931186\pi$
$728$	1222.43	−	3762.25i	0.0622338	−	0.191536i
$729$	2969.39	−	9138.85i	0.150861	−	0.464302i
$730$	−2100.46	+	19984.6i	−0.106495	+	1.01324i
$731$	−21300.9	−	23657.1i	−1.07776	−	1.19698i
$732$	−4778.58	+	5307.15i	−0.241286	+	0.267975i
$733$	−3850.14	−	36631.7i	−0.194009	−	1.84587i	−0.467500	−	0.883993i	$-0.654845\pi$
$733$	−3850.14	−	36631.7i	−0.194009	−	1.84587i	0.273491	−	0.961874i	$-0.411822\pi$
$734$	−21947.2	−	4665.03i	−1.10366	−	0.234591i
$735$	2932.85	−	1305.79i	0.147183	−	0.0655302i
$736$	32427.4	+	23559.9i	1.62404	+	1.17993i
$737$	7147.05	+	3182.07i	0.357212	+	0.159041i
$738$	578.437	+	1001.88i	0.0288517	+	0.0499726i
$739$	−7408.05	+	12831.1i	−0.368754	+	0.638701i	−0.989371	−	0.145413i	$-0.953549\pi$
$739$	−7408.05	+	12831.1i	−0.368754	+	0.638701i	0.620617	+	0.784114i	$0.286882\pi$
$740$	5990.34	−	4352.23i	0.297580	−	0.216204i
$741$	−27330.7	+	5809.32i	−1.35495	+	0.288004i
$742$	−1732.18	−	5331.09i	−0.0857010	−	0.263761i
$743$	11242.2			0.555095			0.277547	−	0.960712i	$-0.410478\pi$
$743$	11242.2			0.555095			0.277547	+	0.960712i	$0.410478\pi$
$744$	−1533.61	−	2732.94i	−0.0755709	−	0.134670i
$745$	−9.68808			−0.000476435
$746$	16530.8	+	50876.6i	0.811308	+	2.49695i
$747$	−5928.35	+	1260.11i	−0.290371	+	0.0617203i
$748$	13320.1	−	9677.64i	0.651112	−	0.473061i
$749$	16217.1	−	28088.8i	0.791133	−	1.37028i
$750$	13024.6	+	22559.2i	0.634120	+	1.09833i
$751$	−9753.49	−	4342.53i	−0.473914	−	0.211000i	0.155859	−	0.987779i	$-0.450186\pi$
$751$	−9753.49	−	4342.53i	−0.473914	−	0.211000i	−0.629773	+	0.776779i	$0.716852\pi$
$752$	3231.39	+	2347.74i	0.156698	+	0.113848i
$753$	15941.4	−	7097.58i	0.771497	−	0.343493i
$754$	−42658.4	−	9067.32i	−2.06038	−	0.437947i
$755$	−317.662	−	3022.35i	−0.0153124	−	0.145688i
$756$	−13571.0	+	15072.1i	−0.652874	+	0.725091i
$757$	11324.3	+	12576.9i	0.543709	+	0.603850i	0.950902	−	0.309492i	$-0.100159\pi$
$757$	11324.3	+	12576.9i	0.543709	+	0.603850i	−0.407193	+	0.913342i	$0.633492\pi$
$758$	−3510.89	+	33403.9i	−0.168234	+	1.60064i
$759$	5258.22	−	16183.1i	0.251464	−	0.773927i
$760$	333.003	−	1024.88i	0.0158938	−	0.0489161i
$761$	−657.096	+	6251.85i	−0.0313005	+	0.297805i	0.967661	+	0.252253i	$0.0811714\pi$
$761$	−657.096	+	6251.85i	−0.0313005	+	0.297805i	−0.998962	+	0.0455521i	$0.985495\pi$
$762$	1816.35	+	2017.27i	0.0863511	+	0.0959026i
$763$	−30152.3	+	33487.5i	−1.43065	+	1.58890i
$764$	12.7038	+	120.869i	0.000601581	+	0.00572366i
$765$	4152.69	+	882.682i	0.196263	+	0.0417169i
$766$	−9608.37	+	4277.92i	−0.453218	+	0.201785i
$767$	34592.5	+	25132.9i	1.62851	+	1.18318i
$768$	17714.7	+	7887.11i	0.832325	+	0.370575i
$769$	−3570.41	−	6184.14i	−0.167428	−	0.289994i	0.770087	−	0.637939i	$-0.220213\pi$
$769$	−3570.41	−	6184.14i	−0.167428	−	0.289994i	−0.937515	+	0.347945i	$0.886880\pi$
$770$	−3746.99	+	6489.98i	−0.175366	+	0.303744i
$771$	−19636.6	+	14266.8i	−0.917242	+	0.666415i
$772$	19610.8	−	4168.40i	0.914259	−	0.194332i
$773$	3179.72	+	9786.18i	0.147952	+	0.455349i	0.997379	−	0.0723575i	$-0.0230523\pi$
$773$	3179.72	+	9786.18i	0.147952	+	0.455349i	−0.849427	+	0.527706i	$0.823052\pi$
$774$	11329.9			0.526154
$775$	2081.50	−	17716.9i	0.0964769	−	0.821176i
$776$	−3103.30			−0.143559
$777$	−7216.79	−	22211.0i	−0.333206	−	1.02550i
$778$	−18189.3	+	3866.25i	−0.838197	+	0.178164i
$779$	1962.71	−	1425.99i	0.0902713	−	0.0655859i
$780$	−7432.21	+	12873.0i	−0.341174	+	0.590931i
$781$	6438.82	+	11152.4i	0.295005	+	0.510964i
$782$	−59105.7	−	26315.6i	−2.70283	−	1.20338i
$783$	15325.9	+	11134.9i	0.699493	+	0.508211i
$784$	−6051.47	+	2694.29i	−0.275668	+	0.122735i
$785$	−2129.50	−	452.639i	−0.0968218	−	0.0205801i
$786$	−2230.77	−	21224.3i	−0.101233	−	0.963163i
$787$	4288.28	−	4762.62i	0.194232	−	0.215717i	−0.638160	−	0.769904i	$-0.720304\pi$
$787$	4288.28	−	4762.62i	0.194232	−	0.215717i	0.832392	+	0.554187i	$0.186971\pi$
$788$	−6814.67	−	7568.46i	−0.308074	−	0.342151i
$789$	−780.317	+	7424.22i	−0.0352092	+	0.334993i
$790$	−3451.29	+	10622.0i	−0.155432	+	0.478371i
$791$	4812.39	−	14811.0i	0.216320	−	0.665764i
$792$	−51.8955	+	493.753i	−0.00232832	+	0.0221524i
$793$	−5565.00	−	6180.56i	−0.249204	−	0.276770i
$794$	−9762.11	+	10841.9i	−0.436328	+	0.484591i
$795$	186.534	+	1774.76i	0.00832162	+	0.0791750i
$796$	−12798.1	−	2720.32i	−0.569869	−	0.121129i
$797$	5161.45	−	2298.03i	0.229395	−	0.102133i	−0.288820	−	0.957383i	$-0.593263\pi$
$797$	5161.45	−	2298.03i	0.229395	−	0.102133i	0.518216	+	0.855250i	$0.326596\pi$
$798$	−32455.2	−	23580.1i	−1.43973	−	1.04602i
$799$	−6496.43	−	2892.40i	−0.287643	−	0.128067i
$800$	−13415.9	−	23237.0i	−0.592905	−	1.02694i
$801$	−1342.46	+	2325.20i	−0.0592177	+	0.102568i
$802$	2599.89	−	1888.93i	0.114471	−	0.0831678i
$803$	−18990.1	+	4036.47i	−0.834553	+	0.177390i
$804$	6884.84	+	21189.4i	0.302002	+	0.929467i
$805$	15375.5			0.673187
$806$	39563.2	−	17038.0i	1.72897	−	0.744587i
$807$	20346.2			0.887510
$808$	1322.59	+	4070.51i	0.0575847	+	0.177228i
$809$	30821.7	−	6551.36i	1.33947	−	0.284714i	0.518206	−	0.855256i	$-0.326600\pi$
$809$	30821.7	−	6551.36i	1.33947	−	0.284714i	0.821269	+	0.570542i	$0.193267\pi$
$810$	13709.3	−	9960.42i	0.594688	−	0.432066i
$811$	−12607.4	+	21836.7i	−0.545878	+	0.945489i	0.452673	+	0.891677i	$0.350471\pi$
$811$	−12607.4	+	21836.7i	−0.545878	+	0.945489i	−0.998551	+	0.0538123i	$0.982863\pi$
$812$	−16346.3	−	28312.6i	−0.706455	−	1.22362i
$813$	−37963.4	−	16902.4i	−1.63768	−	0.729143i
$814$	11084.7	+	8053.51i	0.477296	+	0.346776i
$815$	−2859.30	+	1273.04i	−0.122892	+	0.0547151i
$816$	−34535.7	−	7340.79i	−1.48161	−	0.314925i
$817$	−2483.54	−	23629.3i	−0.106350	−	1.01186i
$818$	23261.7	−	25834.8i	0.994287	−	1.10427i
$819$	7783.24	+	8644.17i	0.332074	+	0.368805i
$820$	134.907	−	1283.55i	0.00574531	−	0.0546629i
$821$	3902.29	−	12010.0i	0.165884	−	0.510539i	−0.833216	−	0.552947i	$-0.813503\pi$
$821$	3902.29	−	12010.0i	0.165884	−	0.510539i	0.999100	+	0.0424083i	$0.0135030\pi$
$822$	17332.2	−	53342.9i	0.735436	−	2.26344i
$823$	−3612.33	+	34369.0i	−0.152999	+	1.45568i	0.601232	+	0.799074i	$0.294677\pi$
$823$	−3612.33	+	34369.0i	−0.152999	+	1.45568i	−0.754231	+	0.656610i	$0.771990\pi$
$824$	−152.935	−	169.852i	−0.00646571	−	0.00718090i
$825$	−7621.89	+	8464.96i	−0.321649	+	0.357227i
$826$	6417.11	+	61054.7i	0.270314	+	2.57187i
$827$	−25027.1	−	5319.68i	−1.05233	−	0.223680i	−0.350898	−	0.936414i	$-0.614124\pi$
$827$	−25027.1	−	5319.68i	−1.05233	−	0.223680i	−0.701435	+	0.712734i	$0.747457\pi$
$828$	10983.3	−	4890.10i	0.460988	−	0.205245i
$829$	−28484.3	−	20695.1i	−1.19337	−	0.867032i	−0.199751	−	0.979847i	$-0.564013\pi$
$829$	−28484.3	−	20695.1i	−1.19337	−	0.867032i	−0.993616	+	0.112814i	$0.964013\pi$
$830$	11830.5	+	5267.30i	0.494752	+	0.220278i
$831$	25604.9	+	44349.0i	1.06886	+	1.85132i
$832$	18359.9	−	31800.3i	0.765043	−	1.32509i
$833$	9541.16	−	6932.06i	0.396857	−	0.288333i
$834$	54890.6	−	11667.3i	2.27902	−	0.484421i
$835$	−3290.20	−	10126.2i	−0.136362	−	0.419678i
$836$	12288.5			0.508382
$837$	−18709.9	−	228.841i	−0.772649	−	0.00945029i
$838$	28283.4			1.16591
$839$	−1605.25	−	4940.44i	−0.0660540	−	0.203293i	0.912582	−	0.408894i	$-0.134085\pi$
$839$	−1605.25	−	4940.44i	−0.0660540	−	0.203293i	−0.978636	+	0.205600i	$0.934085\pi$
$840$	−1768.64	+	375.936i	−0.0726475	+	0.0154417i
$841$	−4973.21	+	3613.25i	−0.203912	+	0.148151i
$842$	13245.2	−	22941.3i	0.542113	−	0.938968i
$843$	−1947.92	−	3373.90i	−0.0795849	−	0.137845i
$844$	42755.9	+	19036.2i	1.74374	+	0.776364i
$845$	−5735.00	−	4166.72i	−0.233479	−	0.169633i
$846$	2312.13	−	1029.42i	0.0939628	−	0.0418349i
$847$	20784.6	+	4417.91i	0.843174	+	0.179222i
$848$	−384.885	−	3661.93i	−0.0155861	−	0.148292i
$849$	−11024.1	+	12243.5i	−0.445636	+	0.494928i
$850$	28980.5	+	32186.1i	1.16944	+	1.29879i
$851$	2938.45	−	27957.5i	0.118365	−	1.12617i
$852$	−11332.7	+	34878.5i	−0.455695	+	1.40248i
$853$	1514.64	−	4661.57i	0.0607973	−	0.187115i	−0.916045	−	0.401076i	$-0.868636\pi$
$853$	1514.64	−	4661.57i	0.0607973	−	0.187115i	0.976842	+	0.213961i	$0.0686364\pi$
$854$	1248.16	−	11875.4i	0.0500129	−	0.475841i
$855$	2120.24	+	2354.77i	0.0848079	+	0.0941887i
$856$	−3072.14	+	3411.95i	−0.122668	+	0.136236i
$857$	−1671.17	−	15900.1i	−0.0666115	−	0.633766i	−0.975993	−	0.217803i	$-0.930111\pi$
$857$	−1671.17	−	15900.1i	−0.0666115	−	0.633766i	0.909381	−	0.415963i	$-0.136556\pi$
$858$	−26904.5	−	5718.73i	−1.07052	−	0.227546i
$859$	13550.9	−	6033.26i	0.538244	−	0.239642i	−0.119565	−	0.992826i	$-0.538150\pi$
$859$	13550.9	−	6033.26i	0.538244	−	0.239642i	0.657809	+	0.753185i	$0.271483\pi$
$860$	−10225.8	−	7429.46i	−0.405460	−	0.294584i
$861$	−3718.76	−	1655.70i	−0.147195	−	0.0655355i
$862$	22530.5	+	39024.0i	0.890247	+	1.54195i
$863$	−10828.2	+	18754.9i	−0.427109	+	0.739774i	−0.996615	−	0.0822133i	$-0.973801\pi$
$863$	−10828.2	+	18754.9i	−0.427109	+	0.739774i	0.569506	+	0.821987i	$0.307134\pi$
$864$	−22769.1	+	16542.7i	−0.896551	+	0.651382i
$865$	−5710.99	+	1213.91i	−0.224485	+	0.0477157i
$866$	2798.48	+	8612.84i	0.109811	+	0.337963i
$867$	33419.6			1.30910
$868$	29336.6	+	13493.8i	1.14718	+	0.527660i
$869$	−10790.5			−0.421222
$870$	6159.95	+	18958.4i	0.240048	+	0.738792i
$871$	−25379.5	+	5394.58i	−0.987315	+	0.209860i
$872$	5160.53	−	3749.35i	0.200410	−	0.145606i
$873$	4562.49	−	7902.47i	0.176881	−	0.306367i
$874$	−24144.5	−	41819.5i	−0.934439	−	1.61850i
$875$	−20774.9	−	9249.58i	−0.802651	−	0.357363i
$876$	−44729.6	−	32498.0i	−1.72520	−	1.25343i
$877$	−40893.7	+	18207.1i	−1.57455	+	0.701037i	−0.993606	−	0.112904i	$-0.963985\pi$
$877$	−40893.7	+	18207.1i	−1.57455	+	0.701037i	−0.580948	+	0.813941i	$0.697318\pi$
$878$	40422.4	+	8592.05i	1.55375	+	0.330259i
$879$	−3270.21	−	31113.9i	−0.125485	−	1.19391i
$880$	−3293.90	+	3658.24i	−0.126179	+	0.140136i
$881$	13949.6	+	15492.6i	0.533455	+	0.592462i	0.948278	−	0.317440i	$-0.102823\pi$
$881$	13949.6	+	15492.6i	0.533455	+	0.592462i	−0.414823	+	0.909902i	$0.636157\pi$
$882$	−438.748	+	4174.41i	−0.0167499	+	0.159365i
$883$	−5552.97	+	17090.3i	−0.211634	+	0.651341i	0.787742	+	0.616005i	$0.211250\pi$
$883$	−5552.97	+	17090.3i	−0.211634	+	0.651341i	−0.999375	+	0.0353358i	$0.988750\pi$
$884$	−16873.9	+	51932.5i	−0.642002	+	1.97588i
$885$	2042.93	−	19437.2i	0.0775959	−	0.738276i
$886$	−10702.7	−	11886.6i	−0.405830	−	0.450720i
$887$	7709.13	−	8561.86i	0.291823	−	0.324103i	−0.579349	−	0.815079i	$-0.696693\pi$
$887$	7709.13	−	8561.86i	0.291823	−	0.324103i	0.871173	+	0.490977i	$0.163360\pi$
$888$	345.560	+	3287.79i	0.0130588	+	0.124247i
$889$	−2317.98	−	492.701i	−0.0874494	−	0.0185879i
$890$	5240.90	−	2333.40i	0.197388	−	0.0878828i
$891$	13245.2	+	9623.20i	0.498015	+	0.361829i
$892$	−8117.87	−	3614.31i	−0.304716	−	0.135668i
$893$	−2653.77	−	4596.47i	−0.0994458	−	0.172245i
$894$	25.5268	−	44.2137i	0.000954970	−	0.00165406i
$895$	4794.34	−	3483.29i	0.179058	−	0.130093i
$896$	8085.05	−	1718.53i	0.301454	−	0.0640760i
$897$	17439.0	+	53671.6i	0.649130	+	1.99782i
$898$	−3080.95			−0.114491
$899$	9670.48	−	28569.0i	0.358764	−	1.05988i
$900$	−8048.22			−0.298082
$901$	2025.78	+	6234.70i	0.0749039	+	0.230530i
$902$	2336.02	−	496.537i	0.0862317	−	0.0183291i
$903$	−32252.6	+	23432.9i	−1.18859	+	0.863563i
$904$	−1102.24	+	1909.14i	−0.0405530	+	0.0702399i
$905$	3275.21	+	5672.82i	0.120300	+	0.208366i
$906$	14630.2	+	6513.76i	0.536484	+	0.238858i
$907$	−11593.4	−	8423.06i	−0.424422	−	0.308361i	0.354992	−	0.934869i	$-0.384483\pi$
$907$	−11593.4	−	8423.06i	−0.424422	−	0.308361i	−0.779415	+	0.626508i	$0.784483\pi$
$908$	−40070.1	+	17840.4i	−1.46451	+	0.652041i
$909$	−12309.9	−	2616.55i	−0.449169	−	0.0954737i
$910$	−2597.94	−	24717.7i	−0.0946383	−	0.900423i
$911$	3891.38	−	4321.82i	0.141523	−	0.157177i	−0.668216	−	0.743967i	$-0.732942\pi$
$911$	3891.38	−	4321.82i	0.141523	−	0.157177i	0.809739	+	0.586790i	$0.199609\pi$
$912$	−17632.9	−	19583.3i	−0.640224	−	0.711041i
$913$	−1307.83	+	12443.2i	−0.0474073	+	0.451050i
$914$	1500.77	−	4618.89i	0.0543118	−	0.167155i
$915$	−1174.71	+	3615.39i	−0.0424424	+	0.130624i
$916$	2207.71	−	21005.0i	0.0796342	−	0.757669i
$917$	12466.5	+	13845.5i	0.448943	+	0.498602i
$918$	30397.9	−	33760.2i	1.09290	−	1.21378i
$919$	384.460	+	3657.89i	0.0137999	+	0.131298i	0.999253	−	0.0386516i	$-0.0123063\pi$
$919$	384.460	+	3657.89i	0.0137999	+	0.131298i	−0.985453	+	0.169949i	$0.945640\pi$
$920$	−2128.93	−	452.518i	−0.0762921	−	0.0162164i
$921$	2902.33	−	1292.20i	0.103838	−	0.0462318i
$922$	2388.13	+	1735.08i	0.0853025	+	0.0619759i
$923$	−39016.5	−	17371.3i	−1.39138	−	0.619482i
$924$	−10309.5	−	17856.7i	−0.367055	−	0.635759i
$925$	−9409.12	+	16297.1i	−0.334454	+	0.579291i
$926$	45.3131	−	32.9219i	0.00160808	−	0.00116834i
$927$	657.369	−	139.728i	0.0232911	−	0.00495068i
$928$	−14019.0	−	43146.1i	−0.495901	−	1.52623i
$929$	21376.7			0.754947			0.377473	−	0.926020i	$-0.376793\pi$
$929$	21376.7			0.754947			0.377473	+	0.926020i	$0.376793\pi$
$930$	−15786.2	−	11767.0i	−0.556613	−	0.414898i
$931$	8802.23			0.309862
$932$	7891.99	+	24289.1i	0.277372	+	0.853664i
$933$	56510.5	−	12011.7i	1.98293	−	0.421484i
$934$	−40559.0	+	29467.9i	−1.42091	+	1.03235i
$935$	4382.10	−	7590.02i	0.153273	−	0.265476i
$936$	−823.279	−	1425.96i	−0.0287497	−	0.0497959i
$937$	41807.8	+	18614.0i	1.45763	+	0.648979i	0.974052	−	0.226322i	$-0.0726702\pi$
$937$	41807.8	+	18614.0i	1.45763	+	0.648979i	0.483578	+	0.875301i	$0.339337\pi$
$938$	−30138.1	−	21896.6i	−1.04909	−	0.762207i
$939$	−8083.61	+	3599.05i	−0.280936	+	0.125081i
$940$	−2761.84	−	587.048i	−0.0958313	−	0.0203696i
$941$	3379.88	+	32157.4i	0.117089	+	1.11403i	0.882443	+	0.470419i	$0.155897\pi$
$941$	3379.88	+	32157.4i	0.117089	+	1.11403i	−0.765354	+	0.643610i	$0.777436\pi$
$942$	7676.66	−	8525.79i	0.265519	−	0.294889i
$943$	−3278.69	−	3641.36i	−0.113223	−	0.125746i
$944$	−4215.27	+	40105.7i	−0.145334	+	1.38276i
$945$	−3336.15	+	10267.6i	−0.114841	+	0.353445i
$946$	7227.59	−	22244.2i	0.248403	−	0.764506i
$947$	2800.80	−	26647.8i	0.0961073	−	0.914400i	−0.835146	−	0.550028i	$-0.814617\pi$
$947$	2800.80	−	26647.8i	0.0961073	−	0.914400i	0.931254	−	0.364372i	$-0.118716\pi$
$948$	−20562.1	−	22836.5i	−0.704457	−	0.782379i
$949$	43083.9	−	47849.6i	1.47372	−	1.63674i
$950$	3378.92	+	32148.3i	0.115397	+	1.09792i
$951$	−54780.2	−	11643.9i	−1.86790	−	0.397034i
$952$	−6068.07	+	2701.68i	−0.206583	+	0.0919767i
$953$	−32425.3	−	23558.4i	−1.10216	−	0.800767i	−0.120750	−	0.992683i	$-0.538530\pi$
$953$	−32425.3	−	23558.4i	−1.10216	−	0.800767i	−0.981411	+	0.191916i	$0.938530\pi$
$954$	−2131.45	−	948.984i	−0.0723358	−	0.0322060i
$955$	32.3468	+	56.0263i	0.00109604	+	0.00189840i
$956$	15006.2	−	25991.5i	0.507672	−	0.879314i
$957$	−15581.0	+	11320.2i	−0.526291	+	0.382373i
$958$	59797.0	−	12710.2i	2.01665	−	0.428653i
$959$	15131.0	+	46568.5i	0.509495	+	1.56807i
$960$	−16784.0			−0.564272
$961$	8510.19	+	28549.6i	0.285663	+	0.958330i
$962$	−45441.1			−1.52295
$963$	−4171.77	−	12839.4i	−0.139599	−	0.429641i
$964$	63889.0	−	13580.0i	2.13457	−	0.453717i
$965$	8633.95	−	6272.93i	0.288017	−	0.209257i
$966$	−40512.4	+	70169.5i	−1.34934	+	2.33713i
$967$	16941.6	+	29343.6i	0.563396	+	0.975831i	0.997197	+	0.0748218i	$0.0238388\pi$
$967$	16941.6	+	29343.6i	0.563396	+	0.975831i	−0.433801	+	0.901009i	$0.642828\pi$
$968$	−2747.87	−	1223.43i	−0.0912394	−	0.0406224i
$969$	37956.3	+	27576.8i	1.25834	+	0.914237i
$970$	−17811.8	+	7930.32i	−0.589590	+	0.262502i
$971$	−29444.2	−	6258.55i	−0.973130	−	0.206845i	−0.306201	−	0.951967i	$-0.599058\pi$
$971$	−29444.2	−	6258.55i	−0.973130	−	0.206845i	−0.666928	+	0.745122i	$0.732391\pi$
$972$	2199.39	+	20925.8i	0.0725777	+	0.690530i
$973$	−32780.8	+	36406.8i	−1.08007	+	1.19953i
$974$	−3574.47	−	3969.85i	−0.117591	−	0.130598i
$975$	3948.83	−	37570.6i	0.129706	−	1.23407i
$976$	2423.84	−	7459.81i	0.0794930	−	0.244654i
$977$	−8447.17	+	25997.7i	−0.276611	+	0.851321i	0.712178	+	0.701999i	$0.247709\pi$
$977$	−8447.17	+	25997.7i	−0.276611	+	0.851321i	−0.988789	+	0.149322i	$0.952291\pi$
$978$	1724.06	−	16403.4i	0.0563696	−	0.536321i
$979$	3708.76	+	4118.99i	0.121075	+	0.134467i
$980$	3133.32	−	3479.91i	0.102133	−	0.113430i
$981$	1960.56	+	18653.5i	0.0638082	+	0.607095i
$982$	−64257.3	−	13658.3i	−2.08812	−	0.443843i
$983$	46012.2	−	20486.0i	1.49294	−	0.664701i	0.511998	−	0.858987i	$-0.328906\pi$
$983$	46012.2	−	20486.0i	1.49294	−	0.664701i	0.980945	+	0.194286i	$0.0622390\pi$
$984$	466.179	+	338.699i	0.0151029	+	0.0109729i
$985$	−4952.51	−	2205.00i	−0.160203	−	0.0713271i
$986$	36614.2	+	63417.6i	1.18259	+	2.04830i
$987$	−4452.80	+	7712.48i	−0.143601	+	0.248724i
$988$	−32971.5	+	23955.2i	−1.06171	+	0.771374i
$989$	−46938.9	+	9977.17i	−1.50917	+	0.320784i
$990$	963.898	+	2966.57i	0.0309441	+	0.0952363i
$991$	34101.8			1.09312			0.546559	−	0.837421i	$-0.315938\pi$
$991$	34101.8			1.09312			0.546559	+	0.837421i	$0.315938\pi$
$992$	35926.8	+	26779.7i	1.14988	+	0.857114i
$993$	35503.8			1.13462
$994$	−18948.7	−	58318.2i	−0.604645	−	1.86091i
$995$	−6812.50	+	1448.04i	−0.217056	+	0.0461367i
$996$	−28826.3	+	20943.6i	−0.917065	+	0.666287i
$997$	−15458.9	+	26775.6i	−0.491061	+	0.850543i	−0.999947	−	0.0102910i	$-0.996724\pi$
$997$	−15458.9	+	26775.6i	−0.491061	+	0.850543i	0.508886	+	0.860834i	$0.330058\pi$
$998$	−17346.3	−	30044.7i	−0.550188	−	0.952954i
$999$	18032.1	+	8028.42i	0.571082	+	0.254262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.7.6	✓	56
31.3	odd	30		961.4.a.l.1.24		28
31.9	even	15	inner	31.4.g.a.9.6	yes	56
31.28	even	15		961.4.a.m.1.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.7.6	✓	56	1.1	even	1	trivial
31.4.g.a.9.6	yes	56	31.9	even	15	inner
961.4.a.l.1.24		28	31.3	odd	30
961.4.a.m.1.24		28	31.28	even	15

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26435 + 3.89127i) q^{2} +(-5.86148 + 1.24590i) q^{3} +(-7.07124 + 5.13756i) q^{4} +(-2.32632 + 4.02930i) q^{5} +(-12.2591 - 21.2333i) q^{6} +(19.5539 + 8.70595i) q^{7} +(-2.45125 - 1.78094i) q^{8} +(8.13897 - 3.62370i) q^{9} +(-18.6204 - 3.95788i) q^{10} +(-1.92247 - 18.2911i) q^{11} +(35.0471 - 38.9237i) q^{12} +(40.8149 + 45.3295i) q^{13} +(-9.15424 + 87.0968i) q^{14} +(8.61558 - 26.5160i) q^{15} +(-17.7769 + 54.7117i) q^{16} +(10.7059 - 101.859i) q^{17} +(24.3913 + 27.0893i) q^{18} +(51.1502 - 56.8080i) q^{19} +(-4.25081 - 40.4438i) q^{20} +(-125.461 - 26.6677i) q^{21} +(68.7449 - 30.6072i) q^{22} +(-124.907 - 90.7499i) q^{23} +(16.5868 + 7.38493i) q^{24} +(51.6765 + 89.5063i) q^{25} +(-124.785 + 216.134i) q^{26} +(87.7037 - 63.7205i) q^{27} +(-182.998 + 38.8973i) q^{28} +(53.9995 + 166.193i) q^{29} +114.074 q^{30} +(-138.386 - 103.152i) q^{31} -259.614 q^{32} +(34.0574 + 104.818i) q^{33} +(409.898 - 87.1266i) q^{34} +(-80.5675 + 58.5357i) q^{35} +(-38.9356 + 67.4385i) q^{36} +(91.0387 + 157.684i) q^{37} +(285.727 + 127.214i) q^{38} +(-295.711 - 214.847i) q^{39} +(12.8783 - 5.73380i) q^{40} +(31.0432 + 6.59844i) q^{41} +(-54.8561 - 521.921i) q^{42} +(207.975 - 230.980i) q^{43} +(107.566 + 119.464i) q^{44} +(-4.33284 + 41.2242i) q^{45} +(195.207 - 600.784i) q^{46} +(21.4556 - 66.0334i) q^{47} +(36.0339 - 342.840i) q^{48} +(77.0491 + 85.5717i) q^{49} +(-282.956 + 314.254i) q^{50} +(64.1541 + 610.386i) q^{51} +(-521.495 - 110.847i) q^{52} +(-58.4726 + 26.0337i) q^{53} +(358.842 + 260.714i) q^{54} +(78.1727 + 34.8047i) q^{55} +(-32.4267 - 56.1647i) q^{56} +(-229.039 + 396.707i) q^{57} +(-578.429 + 420.253i) q^{58} +(685.680 - 145.746i) q^{59} +(75.3048 + 231.764i) q^{60} -136.347 q^{61} +(226.425 - 668.916i) q^{62} +190.696 q^{63} +(-186.027 - 572.531i) q^{64} +(-277.595 + 59.0046i) q^{65} +(-364.814 + 265.053i) q^{66} +(-212.687 + 368.385i) q^{67} +(447.605 + 775.275i) q^{68} +(845.202 + 376.308i) q^{69} +(-329.644 - 239.500i) q^{70} +(-639.647 + 284.789i) q^{71} +(-26.4042 - 5.61239i) q^{72} +(-110.340 - 1049.81i) q^{73} +(-498.485 + 553.623i) q^{74} +(-414.416 - 460.256i) q^{75} +(-69.8407 + 664.490i) q^{76} +(121.650 - 374.399i) q^{77} +(462.144 - 1422.33i) q^{78} +(61.3267 - 583.485i) q^{79} +(-179.095 - 198.906i) q^{80} +(-595.643 + 661.529i) q^{81} +(13.5732 + 129.140i) q^{82} +(-665.419 - 141.439i) q^{83} +(1024.17 - 455.992i) q^{84} +(385.517 + 280.095i) q^{85} +(1161.76 + 517.248i) q^{86} +(-523.577 - 906.862i) q^{87} +(-27.8629 + 48.2599i) q^{88} +(-243.809 + 177.137i) q^{89} +(-165.893 + 35.2616i) q^{90} +(403.453 + 1241.70i) q^{91} +1349.48 q^{92} +(939.662 + 432.211i) q^{93} +284.081 q^{94} +(109.905 + 338.253i) q^{95} +(1521.72 - 323.451i) q^{96} +(828.611 - 602.021i) q^{97} +(-235.565 + 408.011i) q^{98} +(-81.9285 - 141.904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more